{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Derivatives Analytics with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**_Chapters 12 & 13_**\n",
    "\n",
    "**Wiley Finance (2015)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/images/derivatives_analytics_front.jpg\" alt=\"Derivatives Analytics with Python\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dr. Yves J. Hilpisch\n",
    "\n",
    "The Python Quants GmbH\n",
    "\n",
    "<a href='mailto:dawp@tpq.io'>dawp@tpq.io</a> | <a href='http://tpq.io'>http://tpq.io</a>\n",
    "\n",
    "Python online training | <a href='http://training.tpq.io'>http://training.tpq.io</a>\n",
    "\n",
    "DX Analytics library | <a href='http://dx-analytics.com'>http://dx-analytics.com</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import plt\n",
    "plt.style.use('seaborn')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter 12: Valuation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 270\n",
      "         Function evaluations: 485\n"
     ]
    }
   ],
   "source": [
    "%run 12_val/BCC97_simulation.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3225.930, -0.000, 0.147, 0.105, 0.175])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array((S0, r0, kappa_r, theta_r, sigma_r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([22.212, 0.025, 0.952, -0.999, 0.036, 0.008, -0.501, 0.000])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZXlwuFxUd1cSGB8d8M/Bhz5kxJga4D/iatfbbQJExZtMph30VqLfWfhf4b+B+z7kJwNet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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108d6dbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rate_paths(r)\n",
    "plt.savefig('../images/12_val/rate_paths.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7PoaZz6P7ty9kU9kCs4tpThzpRtc0BrtDaFr9NWe5ksnTMTv6Jp4+gnAzGTel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VqCzm3TCUaj+to1GavdYHqtHgRBYy2b0tW6bvdb2jlLnzsDqornyBH9BlEsdxEr4TGKM/M9ng+n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\niK2ru/xc7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FXl8tlFJKvIrv0dNb/3WS0UVY3R2BRzqQUOtuzlkZ7jwHo+oiAItHX6SCXy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WxdpOieGwh/CACozs8dDwyIRrZutw3AlDr2FoxZ6qGcBUPEC67Mctdys2nWsnMiDCCUDrIwoo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gTHcVxqE4lKIreyniS0scGgdIRnX95/9H3hvZKzYrH4R4vF4n9fLBb/WrFY/C8n/D5cLBb/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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a940908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_volatility_paths(v)\n",
    "plt.savefig('../images/12_val/volatility_paths.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Rs7uoNr+ae+v3XPfj0C5Hd6iPLxz8Oxw2J5+4+cNU5PoXXS/RZIyuUI8Zyia6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\n5KvtjAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10be24c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_index_paths(S)\n",
    "plt.savefig('../images/12_val/ES50_paths.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TJElqlEFNkiSpUQY1SZKkRhnUJEmSGuWzPiVpEnq8zxxdPH/eOFUiqZ/sUZMkSWqUQU2S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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bf56fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_index_histogram(S)\n",
    "plt.savefig('../images/12_val/ES50_histogram.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### European Options Valuation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c79eeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run 12_val/BCC97_valuation_comparison.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      C0 |     MCS |    DIFF\n",
      "  0.083 |   3050 | 193.692 | 195.584 |   1.892\n",
      "  0.083 |   3225 |  62.147 |  64.162 |   2.016\n",
      "  0.083 |   3400 |   1.967 |   2.544 |   0.577\n",
      "  0.500 |   3050 | 259.126 | 272.960 |  13.834\n",
      "  0.500 |   3225 | 146.891 | 164.333 |  17.443\n",
      "  0.500 |   3400 |  67.142 |  85.330 |  18.188\n",
      "  1.000 |   3050 | 321.419 | 344.280 |  22.861\n",
      "  1.000 |   3225 | 216.227 | 243.415 |  27.188\n",
      "  1.000 |   3400 | 133.950 | 162.403 |  28.453\n",
      "  1.500 |   3050 | 378.978 | 407.035 |  28.057\n",
      "  1.500 |   3225 | 276.942 | 309.251 |  32.309\n",
      "  1.500 |   3400 | 193.333 | 227.887 |  34.554\n",
      "  2.000 |   3050 | 435.337 | 470.659 |  35.322\n",
      "  2.000 |   3225 | 335.010 | 374.315 |  39.305\n",
      "  2.000 |   3400 | 250.314 | 291.888 |  41.574\n",
      "  3.000 |   3050 | 549.127 | 594.413 |  45.287\n",
      "  3.000 |   3225 | 450.522 | 499.873 |  49.350\n",
      "  3.000 |   3400 | 364.049 | 416.300 |  52.252\n",
      "CPU times: user 5.56 s, sys: 1.18 s, total: 6.74 s\n",
      "Wall time: 6.28 s\n"
     ]
    }
   ],
   "source": [
    "%time compare_values(M0=50, I=50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      C0 |     MCS |    DIFF\n",
      "  0.083 |   3050 | 193.692 | 195.870 |   2.178\n",
      "  0.083 |   3225 |  62.147 |  64.609 |   2.462\n",
      "  0.083 |   3400 |   1.967 |   2.606 |   0.639\n",
      "  0.500 |   3050 | 259.126 | 273.046 |  13.920\n",
      "  0.500 |   3225 | 146.891 | 164.698 |  17.807\n",
      "  0.500 |   3400 |  67.142 |  85.852 |  18.710\n",
      "  1.000 |   3050 | 321.419 | 342.696 |  21.277\n",
      "  1.000 |   3225 | 216.227 | 241.375 |  25.148\n",
      "  1.000 |   3400 | 133.950 | 160.706 |  26.756\n",
      "  1.500 |   3050 | 378.978 | 407.341 |  28.363\n",
      "  1.500 |   3225 | 276.942 | 309.124 |  32.182\n",
      "  1.500 |   3400 | 193.333 | 227.473 |  34.140\n",
      "  2.000 |   3050 | 435.337 | 470.323 |  34.986\n",
      "  2.000 |   3225 | 335.010 | 373.940 |  38.930\n",
      "  2.000 |   3400 | 250.314 | 291.583 |  41.268\n",
      "  3.000 |   3050 | 549.127 | 597.571 |  48.444\n",
      "  3.000 |   3225 | 450.522 | 503.362 |  52.840\n",
      "  3.000 |   3400 | 364.049 | 420.019 |  55.970\n",
      "CPU times: user 22.7 s, sys: 6.31 s, total: 29 s\n",
      "Wall time: 27.4 s\n"
     ]
    }
   ],
   "source": [
    "%time compare_values(M0=50, I=200000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      C0 |     MCS |    DIFF\n",
      "  0.083 |   3050 | 193.692 | 193.241 |  -0.450\n",
      "  0.083 |   3225 |  62.147 |  61.595 |  -0.552\n",
      "  0.083 |   3400 |   1.967 |   2.581 |   0.614\n",
      "  0.500 |   3050 | 259.126 | 259.140 |   0.014\n",
      "  0.500 |   3225 | 146.891 | 149.090 |   2.199\n",
      "  0.500 |   3400 |  67.142 |  71.122 |   3.980\n",
      "  1.000 |   3050 | 321.419 | 322.117 |   0.697\n",
      "  1.000 |   3225 | 216.227 | 219.528 |   3.301\n",
      "  1.000 |   3400 | 133.950 | 139.285 |   5.335\n",
      "  1.500 |   3050 | 378.978 | 377.499 |  -1.479\n",
      "  1.500 |   3225 | 276.942 | 278.276 |   1.334\n",
      "  1.500 |   3400 | 193.333 | 197.137 |   3.804\n",
      "  2.000 |   3050 | 435.337 | 435.067 |  -0.270\n",
      "  2.000 |   3225 | 335.010 | 337.597 |   2.587\n",
      "  2.000 |   3400 | 250.314 | 255.541 |   5.227\n",
      "  3.000 |   3050 | 549.127 | 552.842 |   3.715\n",
      "  3.000 |   3225 | 450.522 | 457.774 |   7.252\n",
      "  3.000 |   3400 | 364.049 | 374.340 |  10.291\n",
      "CPU times: user 21.7 s, sys: 5.14 s, total: 26.9 s\n",
      "Wall time: 25.5 s\n"
     ]
    }
   ],
   "source": [
    "%time compare_values(M0=200, I=50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### American Options Valuation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run 12_val/BCC97_american_valuation.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      P0 |     LSM |    DIFF\n",
      "  0.083 |   3050 |  17.681 |  17.431 |  -0.250\n",
      "  0.083 |   3225 |  61.131 |  61.001 |  -0.130\n",
      "  0.083 |   3400 | 175.947 | 181.570 |   5.623\n",
      "  0.500 |   3050 |  77.963 |  84.277 |   6.314\n",
      "  0.500 |   3225 | 140.428 | 149.270 |   8.842\n",
      "  0.500 |   3400 | 235.379 | 246.150 |  10.771\n",
      "  1.000 |   3050 | 124.220 | 136.155 |  11.934\n",
      "  1.000 |   3225 | 192.808 | 207.958 |  15.149\n",
      "  1.000 |   3400 | 284.311 | 302.051 |  17.740\n",
      "  1.500 |   3050 | 155.970 | 174.854 |  18.884\n",
      "  1.500 |   3225 | 226.234 | 250.278 |  24.044\n",
      "  1.500 |   3400 | 314.923 | 344.215 |  29.292\n",
      "  2.000 |   3050 | 177.841 | 206.460 |  28.619\n",
      "  2.000 |   3225 | 247.834 | 282.910 |  35.077\n",
      "  2.000 |   3400 | 333.458 | 376.640 |  43.182\n",
      "  3.000 |   3050 | 201.032 | 249.858 |  48.826\n",
      "  3.000 |   3225 | 267.549 | 328.487 |  60.937\n",
      "  3.000 |   3400 | 346.197 | 421.464 |  75.267\n",
      "CPU times: user 39.8 s, sys: 7.42 s, total: 47.2 s\n",
      "Wall time: 43.5 s\n"
     ]
    }
   ],
   "source": [
    "%time lsm_compare_values(M0=150, I=50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter 13: Dynamic Hedging"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BSM Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run 13_dyh/BSM_lsm_hedging_algorithm.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "APPROXIMATION OF FIRST ORDER \n",
      "-----------------------------\n",
      "    step |     S_t |   Delta \n",
      "       1 |   34.97 |   -0.79\n",
      "       2 |   36.14 |   -0.70\n",
      "       3 |   36.40 |   -0.67\n",
      "       4 |   37.61 |   -0.59\n",
      "       5 |   37.41 |   -0.59\n",
      "          wrong\n",
      "       6 |   38.52 |   -0.54\n",
      "       7 |   39.43 |   -0.48\n",
      "       8 |   40.09 |   -0.43\n",
      "       9 |   40.07 |   -0.41\n",
      "          wrong\n",
      "      10 |   41.79 |   -0.32\n",
      "      11 |   41.26 |   -0.33\n",
      "      12 |   40.22 |   -0.38\n",
      "      13 |   38.42 |   -0.51\n",
      "      14 |   37.98 |   -0.57\n",
      "      15 |   36.79 |   -0.68\n",
      "      16 |   35.86 |   -0.78\n",
      "      17 |   34.49 |   -0.90\n",
      "      18 |   34.48 |   -0.90\n",
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BSM)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.995\n",
      "Bonds                40.303\n",
      "Cost                  4.474\n",
      "\n",
      "Regular Rehedges \n",
      "--------------------------------------------------------------------\n",
      "step|     S_t|    Port|     Put|    Diff|   Stock|    Bond|    Cost|\n",
      "   1|  34.968|   5.549|   5.215|   0.334|  -0.789|  33.156|   5.549|\n",
      "   2|  36.145|   4.660|   4.369|   0.291|  -0.700|  29.956|   4.660|\n",
      "   3|  36.398|   4.518|   4.181|   0.337|  -0.671|  28.926|   4.518|\n",
      "   4|  37.614|   3.738|   3.452|   0.286|  -0.590|  25.944|   3.738|\n",
      "   5|  37.415|   3.887|   3.550|   0.336|  -0.587|  25.833|   3.887|\n",
      "   6|  38.519|   3.270|   2.968|   0.301|  -0.538|  23.979|   3.270|\n",
      "   7|  39.430|   2.809|   2.539|   0.270|  -0.477|  21.624|   2.809|\n",
      "   8|  40.090|   2.520|   2.277|   0.243|  -0.434|  19.911|   2.520|\n",
      "   9|  40.071|   2.552|   2.267|   0.285|  -0.414|  19.153|   2.552|\n",
      "  10|  41.790|   1.863|   1.641|   0.221|  -0.322|  15.309|   1.863|\n",
      "  11|  41.262|   2.051|   1.830|   0.221|  -0.330|  15.666|   2.051|\n",
      "  12|  40.217|   2.415|   2.198|   0.217|  -0.376|  17.528|   2.415|\n",
      "  13|  38.419|   3.111|   3.026|   0.085|  -0.515|  22.880|   3.111|\n",
      "  14|  37.980|   3.365|   3.247|   0.118|  -0.569|  24.966|   3.365|\n",
      "  15|  36.795|   4.069|   3.959|   0.110|  -0.679|  29.062|   4.069|\n",
      "  16|  35.858|   4.740|   4.531|   0.209|  -0.778|  32.623|   4.740|\n",
      "  17|  34.488|   5.844|   5.616|   0.229|  -0.898|  36.805|   5.844|\n",
      "  18|  34.477|   5.899|   5.623|   0.276|  -0.905|  37.091|   5.899|\n",
      "MSE               0.061\n",
      "Average Error     0.230\n",
      "Total P&L         4.370\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BSM_hedge_run(p=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PwH3fMApuvgUjMSnS4YkYEGigyFr9LsnXdiV+1qOYs7NxPzKjWk4WKqJXee/Ge4G2wGda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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c711ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t)\n",
    "# plt.savefig('../images/13_dyh/BSM_hedge_run_1.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "APPROXIMATION OF FIRST ORDER \n",
      "-----------------------------\n",
      "    step |     S_t |   Delta \n",
      "       1 |   35.31 |   -0.75\n",
      "       2 |   36.25 |   -0.69\n",
      "       3 |   37.50 |   -0.61\n",
      "       4 |   35.98 |   -0.69\n",
      "       5 |   36.52 |   -0.65\n",
      "       6 |   35.98 |   -0.70\n",
      "       7 |   35.55 |   -0.75\n",
      "       8 |   35.89 |   -0.72\n",
      "       9 |   38.18 |   -0.53\n",
      "      10 |   38.25 |   -0.52\n",
      "      11 |   38.00 |   -0.54\n",
      "      12 |   37.80 |   -0.56\n",
      "      13 |   39.22 |   -0.45\n",
      "      14 |   39.54 |   -0.44\n",
      "      15 |   39.82 |   -0.42\n",
      "      16 |   39.29 |   -0.46\n",
      "      17 |   38.11 |   -0.56\n",
      "      18 |   38.10 |   -0.57\n",
      "      19 |   39.61 |   -0.43\n",
      "      20 |   40.22 |   -0.39\n",
      "      21 |   39.78 |   -0.43\n",
      "      22 |   39.90 |   -0.42\n",
      "      23 |   39.82 |   -0.44\n",
      "      24 |   41.30 |   -0.32\n",
      "      25 |   42.60 |   -0.23\n",
      "      26 |   42.86 |   -0.21\n",
      "      27 |   44.64 |   -0.13\n",
      "      28 |   42.78 |   -0.22\n",
      "      29 |   42.22 |   -0.26\n",
      "      30 |   42.15 |   -0.27\n",
      "      31 |   41.36 |   -0.33\n",
      "      32 |   44.03 |   -0.14\n",
      "      33 |   45.28 |   -0.08\n",
      "      34 |   44.03 |   -0.14\n",
      "      35 |   43.86 |   -0.15\n",
      "      36 |   44.61 |   -0.10\n",
      "      37 |   46.20 |   -0.02\n",
      "      38 |   46.10 |   -0.02\n",
      "          wrong\n",
      "      39 |   44.46 |   -0.10\n",
      "      40 |   43.52 |   -0.15\n",
      "      41 |   42.29 |   -0.26\n",
      "      42 |   42.84 |   -0.21\n",
      "      43 |   41.33 |   -0.36\n",
      "      44 |   42.18 |   -0.27\n",
      "      45 |   41.95 |   -0.28\n",
      "      46 |   40.84 |   -0.41\n",
      "      47 |   40.71 |   -0.42\n",
      "      48 |   40.80 |   -0.42\n",
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BSM)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.995\n",
      "Bonds                40.303\n",
      "Cost                  4.474\n",
      "\n",
      "Regular Rehedges \n",
      "--------------------------------------------------------------------\n",
      "step|     S_t|    Port|     Put|    Diff|   Stock|    Bond|    Cost|\n",
      "   1|  35.308|   5.211|   4.945|   0.266|  -0.747|  31.602|   5.211|\n",
      "   2|  36.252|   4.543|   4.297|   0.246|  -0.692|  29.618|   4.543|\n",
      "   3|  37.503|   3.713|   3.500|   0.213|  -0.607|  26.487|   3.713|\n",
      "   4|  35.983|   4.668|   4.481|   0.187|  -0.690|  29.499|   4.668|\n",
      "   5|  36.517|   4.335|   4.089|   0.246|  -0.654|  28.211|   4.335|\n",
      "   6|  35.979|   4.720|   4.492|   0.228|  -0.703|  30.005|   4.720|\n",
      "   7|  35.548|   5.059|   4.817|   0.242|  -0.754|  31.879|   5.059|\n",
      "   8|  35.887|   4.842|   4.552|   0.290|  -0.715|  30.512|   4.842|\n",
      "   9|  38.183|   3.236|   3.134|   0.103|  -0.526|  23.311|   3.236|\n",
      "  10|  38.251|   3.229|   3.074|   0.154|  -0.518|  23.052|   3.229|\n",
      "  11|  38.001|   3.386|   3.257|   0.129|  -0.543|  24.017|   3.386|\n",
      "  12|  37.801|   3.523|   3.327|   0.196|  -0.563|  24.787|   3.523|\n",
      "  13|  39.224|   2.752|   2.637|   0.115|  -0.447|  20.296|   2.752|\n",
      "  14|  39.537|   2.637|   2.487|   0.150|  -0.445|  20.219|   2.637|\n",
      "  15|  39.821|   2.535|   2.377|   0.158|  -0.416|  19.091|   2.535|\n",
      "  16|  39.290|   2.779|   2.591|   0.187|  -0.460|  20.858|   2.779|\n",
      "  17|  38.107|   3.348|   3.171|   0.177|  -0.564|  24.859|   3.348|\n",
      "  18|  38.095|   3.385|   3.187|   0.198|  -0.567|  24.995|   3.385|\n",
      "  19|  39.614|   2.553|   2.456|   0.097|  -0.432|  19.653|   2.553|\n",
      "  20|  40.221|   2.315|   2.214|   0.101|  -0.392|  18.099|   2.315|\n",
      "  21|  39.775|   2.511|   2.394|   0.117|  -0.433|  19.733|   2.511|\n",
      "  22|  39.904|   2.479|   2.333|   0.147|  -0.424|  19.417|   2.479|\n",
      "  23|  39.821|   2.538|   2.361|   0.176|  -0.436|  19.895|   2.538|\n",
      "  24|  41.296|   1.919|   1.825|   0.094|  -0.318|  15.071|   1.919|\n",
      "  25|  42.603|   1.521|   1.431|   0.090|  -0.230|  11.316|   1.521|\n",
      "  26|  42.863|   1.474|   1.350|   0.124|  -0.208|  10.385|   1.474|\n",
      "  27|  44.637|   1.118|   0.962|   0.156|  -0.129|   6.894|   1.118|\n",
      "  28|  42.777|   1.367|   1.370|  -0.003|  -0.216|  10.598|   1.367|\n",
      "  29|  42.225|   1.499|   1.538|  -0.039|  -0.258|  12.386|   1.499|\n",
      "  30|  42.148|   1.533|   1.562|  -0.029|  -0.266|  12.750|   1.533|\n",
      "  31|  41.361|   1.758|   1.805|  -0.046|  -0.327|  15.284|   1.758|\n",
      "  32|  44.033|   0.903|   1.091|  -0.188|  -0.141|   7.114|   0.903|\n",
      "  33|  45.279|   0.736|   0.848|  -0.112|  -0.077|   4.225|   0.736|\n",
      "  34|  44.028|   0.837|   1.075|  -0.238|  -0.137|   6.880|   0.837|\n",
      "  35|  43.862|   0.868|   1.120|  -0.252|  -0.146|   7.279|   0.868|\n",
      "  36|  44.608|   0.768|   0.976|  -0.208|  -0.101|   5.283|   0.768|\n",
      "  37|  46.195|   0.614|   0.705|  -0.092|  -0.024|   1.740|   0.614|\n",
      "  38|  46.097|   0.618|   0.711|  -0.093|  -0.021|   1.605|   0.618|\n",
      "  39|  44.460|   0.655|   0.999|  -0.344|  -0.096|   4.941|   0.655|\n",
      "  40|  43.522|   0.751|   1.199|  -0.448|  -0.152|   7.363|   0.751|\n",
      "  41|  42.289|   0.948|   1.514|  -0.567|  -0.261|  11.966|   0.948|\n",
      "  42|  42.839|   0.819|   1.366|  -0.548|  -0.211|   9.871|   0.819|\n",
      "  43|  41.327|   1.150|   1.797|  -0.647|  -0.358|  15.932|   1.150|\n",
      "  44|  42.176|   0.865|   1.522|  -0.656|  -0.268|  12.158|   0.865|\n",
      "  45|  41.953|   0.940|   1.606|  -0.667|  -0.283|  12.819|   0.940|\n",
      "  46|  40.844|   1.269|   1.965|  -0.696|  -0.407|  17.911|   1.269|\n",
      "  47|  40.713|   1.344|   1.995|  -0.651|  -0.424|  18.590|   1.344|\n",
      "  48|  40.797|   1.331|   1.907|  -0.576|  -0.416|  18.300|   1.331|\n",
      "MSE               0.093\n",
      "Average Error    -0.051\n",
      "Total P&L        -2.512\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BSM_hedge_run(p=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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F3uaX4mvQqFSFyREMg4xX3yB64gSiZr1OfJ8H8E15nuxhj4cWOS2jCQ7t69dh3bWTnLu6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\nzM3h4PWSMn0KwbFjMXw+cu7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3RSsCNc8IX2DBII7lS/GffQ5HVGBFZPlrN0lXt8K16G08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\niIjojf8AVydg9cC2UxwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c6d72e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t)\n",
    "plt.savefig('../images/13_dyh/BSM_hedge_run_2.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c7b8d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run 13_dyh/BSM_lsm_hedging_histogram.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of American Put Option is    4.493\n",
      "Delta t=0 is                      -0.406\n",
      "run  1000   p/l    0.339\n",
      "run  2000   p/l   -0.067\n",
      "run  3000   p/l    0.379\n",
      "run  4000   p/l   -0.029\n",
      "run  5000   p/l    0.286\n",
      "run  6000   p/l    0.244\n",
      "run  7000   p/l   -0.761\n",
      "run  8000   p/l   -0.761\n",
      "run  9000   p/l   -0.002\n",
      "run 10000   p/l   -0.257\n",
      "\n",
      "SUMMARY STATISTICS FOR P&L\n",
      "---------------------------------\n",
      "Dynamic Replications        10000\n",
      "Time Steps                     50\n",
      "Paths for Valuation         10000\n",
      "Maximum                     5.447\n",
      "Average                     0.041\n",
      "Median                      0.036\n",
      "Minimum                   -11.475\n",
      "---------------------------------\n",
      "CPU times: user 6.2 s, sys: 669 ms, total: 6.87 s\n",
      "Wall time: 6.37 s\n"
     ]
    }
   ],
   "source": [
    "%time pl_list = BSM_dynamic_hedge_mcs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Sc+k+zMz/6mbZSPJ0uv9/Pkc30Hgk3Qe6F/Dd/t4B/F6SW+mO8cnTqXYktgEn\nJvkBuhH7l4F30/VzSR5fZ9CTJKlxnsaXJKlxhr0kSY0z7CVJapxhL0lS4wx7SZIa50/vJA0tybPo\npgD9e+ARwKPo5rD/aJJjgfPmz/Of5Pl0UzqvAl5eVfsgaaIc2UvaGy8GPlBVL6e7udIr6WZD253n\nAR+uqgfNqiZpMvydvdS4JL9KdxOkP6e72c6P0k1is7Nv/xPgELrb7J4G3Aj8Dt1EIT9EdyvSj/Uz\n3Z1Pd8vOvwY+DLypf9630t3V698AHwT+sqre3c/4dxPwY/2Nmx7YNbJPcgTdWYLbgMfTzTX++SRr\n6SZkuYVuLvGbquriJEcDv9G3Pwn4g6q6aixvmtQYR/ZS46rq7XR3x/vHqvp14AS628p+mm42uydU\n1YvoRuC30YX/e6rqVcCvAX+c5DFV9QG62y6/q6rOrKpP0gU9/fz2bwH+oap+vare3b/80+mmCd05\nWFM/1fMHgQv61/lN4IP9PcBPBrZU1TnAf+a7/0+dQ3dW4TV9/YPzjkvaDcNeWjmuhW4qV7ppTdf1\n7R/v2/+Sbv75nxzYdivwFR76fbifR3cGYL6nAHNV9df963yRborVHwU+Cbwgybvobun8u/0+V9BN\nP/u7wGz/4UPSEAx7SffteZOH7KdZ+IY9i35/WFWfp/ta4cN01wR8pG//Q+BwurMP7+7vJS5pCIa9\ntHLsugPXAcBP0N2w5HtU1Xa6Uf3R/bazwMHAp4Z4/m/RXXFPkl9K8jhgR3924EEvBWxJcni//VOA\ne4AvJPll4Ier6r10N0Q6st/mYuCfquqtdB8C/u2Q/ZZWPH96J60cj0zyP4AAF9BdFHckcHCSr1fV\nFf12pwDrkxxDF/Qvrqo7+wv0dm2/k+70/gkAST4JfAbYJ8nlwK10p+A/suvFk1zS//mmqnpVkhcA\n5yb5MvCDwAur6r4k/wi8KckXgYPoLsoDuJvuTnlfBp4A/Pbo3yKpTV6NL60AfRif119UN6nX/Ahw\nVv99vKQp8jS+1LgkpwNPBl6Z5OAJvvSVBr20NDiylySpcY7sJUlqnGEvSVLjDHtJkhpn2EuS1DjD\nXpKkxhn2kiQ17v8DyMwwW30+T2AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c6b7d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_histogram(pl_list)\n",
    "plt.savefig('../images/13_dyh/BSM_hedge_histo.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of American Put Option is    4.471\n",
      "Delta t=0 is                      -1.001\n",
      "run  1000   p/l   -0.024\n",
      "run  2000   p/l    0.062\n",
      "run  3000   p/l    0.179\n",
      "run  4000   p/l    0.343\n",
      "run  5000   p/l   -0.012\n",
      "run  6000   p/l   -0.193\n",
      "run  7000   p/l   -0.117\n",
      "run  8000   p/l   -0.334\n",
      "run  9000   p/l   -0.025\n",
      "run 10000   p/l   -0.000\n",
      "\n",
      "SUMMARY STATISTICS FOR P&L\n",
      "---------------------------------\n",
      "Dynamic Replications        10000\n",
      "Time Steps                    200\n",
      "Paths for Valuation        150000\n",
      "Maximum                     2.232\n",
      "Average                     0.003\n",
      "Median                      0.014\n",
      "Minimum                    -1.284\n",
      "---------------------------------\n",
      "CPU times: user 41.9 s, sys: 4.28 s, total: 46.2 s\n",
      "Wall time: 43.6 s\n"
     ]
    }
   ],
   "source": [
    "%time pl_list = BSM_dynamic_hedge_mcs(M=200, I=150000) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1099392e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_histogram(pl_list)\n",
    "plt.savefig('../images/13_dyh/BSM_hedge_histo_more.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BCC97 Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bc2ea90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run 13_dyh/BCC97_lsm_hedging_algorithm.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BCC97)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.426\n",
      "Bonds              1602.498\n",
      "Cost                228.305\n",
      "\n",
      "Regular Rehedges \n",
      "----------------------------------------------------------------------------------\n",
      "step|       S_t|      Port|       Put|      Diff|     Stock|      Bond|      Cost|\n",
      "   1|  3293.090|   199.691|   201.600|    -1.909|    -1.856|  6311.671|   199.691|\n",
      "   2|  3323.629|   143.027|   186.740|   -43.712|    -0.318|  1201.164|   143.027|\n",
      "   3|  3352.073|   133.986|   175.533|   -41.547|    -0.358|  1335.491|   133.986|\n",
      "   4|  3380.280|   123.907|   163.659|   -39.752|    -0.429|  1572.798|   123.907|\n",
      "   5|  3370.652|   128.084|   165.605|   -37.521|    -0.401|  1481.094|   128.084|\n",
      "   6|  3398.985|   116.788|   153.569|   -36.781|    -0.381|  1410.163|   116.788|\n",
      "   7|  3369.633|   128.053|   160.805|   -32.752|    -0.408|  1503.294|   128.053|\n",
      "   8|  3289.659|   160.744|   187.601|   -26.858|    -0.437|  1598.083|   160.744|\n",
      "   9|  3286.331|   162.201|   184.473|   -22.272|    -0.472|  1714.368|   162.201|\n",
      "  10|  3072.690|   263.123|   284.850|   -21.728|    -0.615|  2153.371|   263.123|\n",
      "  11|  3062.960|   269.162|   286.396|   -17.234|    -0.620|  2169.351|   269.162|\n",
      "  12|  3089.016|   253.057|   269.050|   -15.993|    -0.586|  2062.950|   253.057|\n",
      "  13|  3131.731|   228.088|   244.894|   -16.806|    -0.605|  2122.716|   228.088|\n",
      "  14|  2919.759|   356.410|   374.043|   -17.633|    -0.719|  2456.331|   356.410|\n",
      "  15|  2924.716|   352.992|   368.183|   -15.190|    -0.715|  2445.309|   352.992|\n",
      "  16|  2985.576|   309.674|   324.159|   -14.485|    -0.674|  2322.644|   309.674|\n",
      "  17|  3010.488|   293.137|   305.393|   -12.257|    -0.671|  2312.873|   293.137|\n",
      "  18|  3035.974|   276.272|   286.501|   -10.229|    -0.664|  2291.587|   276.272|\n",
      "  19|  2969.817|   320.364|   328.519|    -8.155|    -0.717|  2450.217|   320.364|\n",
      "  20|  2955.277|   330.957|   336.499|    -5.543|    -0.730|  2488.901|   330.957|\n",
      "  21|  2910.463|   363.812|   367.966|    -4.154|    -0.775|  2619.850|   363.812|\n",
      "  22|  2936.027|   344.124|   347.962|    -3.838|    -0.763|  2585.737|   344.124|\n",
      "  23|  2987.578|   304.899|   306.569|    -1.671|    -0.743|  2525.017|   304.899|\n",
      "  24|  3041.506|   264.946|   268.346|    -3.400|    -0.724|  2466.747|   264.946|\n",
      "  25|  3066.863|   246.702|   248.523|    -1.820|    -0.713|  2433.393|   246.702|\n",
      "  26|  3085.940|   233.253|   234.646|    -1.393|    -0.731|  2489.226|   233.253|\n",
      "  27|  2942.050|   338.668|   331.666|     7.002|    -0.807|  2712.051|   338.668|\n",
      "  28|  3004.776|   288.394|   282.345|     6.049|    -0.784|  2644.029|   288.394|\n",
      "  29|  2970.714|   315.412|   304.896|    10.517|    -0.800|  2693.090|   315.412|\n",
      "  30|  2925.292|   352.084|   340.969|    11.115|    -0.834|  2792.550|   352.084|\n",
      "  31|  2950.434|   331.659|   316.799|    14.860|    -0.825|  2764.770|   331.659|\n",
      "  32|  2975.783|   311.372|   293.654|    17.718|    -0.817|  2742.629|   311.372|\n",
      "  33|  3000.930|   291.387|   270.351|    21.036|    -0.824|  2765.407|   291.387|\n",
      "  34|  3026.450|   271.055|   249.040|    22.015|    -0.835|  2799.472|   271.055|\n",
      "  35|  3052.321|   250.229|   226.402|    23.827|    -0.846|  2831.893|   250.229|\n",
      "  36|  3040.977|   260.583|   232.051|    28.531|    -0.865|  2890.750|   260.583|\n",
      "  37|  2944.367|   344.821|   312.481|    32.340|    -0.891|  2968.693|   344.821|\n",
      "  38|  2969.569|   323.101|   286.949|    36.151|    -0.885|  2950.267|   323.101|\n",
      "  39|  3063.118|   241.251|   203.197|    38.053|    -0.878|  2931.744|   241.251|\n",
      "  40|  3086.580|   221.609|   182.630|    38.979|    -0.890|  2967.876|   221.609|\n",
      "  41|  3120.600|   192.468|   154.231|    38.237|    -0.899|  2998.923|   192.468|\n",
      "  42|  3087.541|   223.555|   173.331|    50.224|    -0.921|  3067.014|   223.555|\n",
      "  43|  3114.275|   200.330|   148.137|    52.193|    -0.922|  3072.192|   200.330|\n",
      "  44|  3171.573|   148.889|   105.082|    43.807|    -0.925|  3083.025|   148.889|\n",
      "  45|  3216.916|   108.229|    75.952|    32.278|    -0.931|  3102.564|   108.229|\n",
      "  46|  3089.488|   228.041|   152.105|    75.936|    -0.949|  3159.463|   228.041|\n",
      "  47|  2993.663|   320.436|   241.184|    79.252|    -0.964|  3205.245|   320.436|\n",
      "  48|  2852.621|   457.738|   377.569|    80.168|    -0.973|  3233.375|   457.738|\n",
      "  49|  2931.133|   382.376|   295.071|    87.305|    -0.990|  3283.929|   382.376|\n",
      "  50|  2872.067|   441.749|   353.863|    87.886|     0.000|  3283.929|  3283.929|\n",
      "MSE             1268.777\n",
      "Average Error     9.428\n",
      "Total P&L       480.848\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BCC97_hedge_run(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Z4aC1diqlCvzTWmu9i8Csqf86ae+P1vrlk7RvA/oUIlZRBribBdfDWbeWvOvaGRyNEEIY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\ndUxwJElS6/w/l23lzrOcDg8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109939c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_run_1.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BCC97)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.426\n",
      "Bonds              1602.498\n",
      "Cost                228.305\n",
      "\n",
      "Regular Rehedges \n",
      "----------------------------------------------------------------------------------\n",
      "step|       S_t|      Port|       Put|      Diff|     Stock|      Bond|      Cost|\n",
      "   1|  3313.460|   191.013|   193.940|    -2.927|    -1.821|  6224.627|   191.013|\n",
      "   2|  3358.312|   109.360|   174.333|   -64.973|    -0.312|  1158.262|   109.360|\n",
      "   3|  3387.038|   100.396|   163.691|   -63.295|    -0.348|  1278.376|   100.396|\n",
      "   4|  3446.356|    79.780|   143.499|   -63.719|    -0.333|  1226.302|    79.780|\n",
      "   5|  3505.434|    60.134|   125.819|   -65.685|    -0.287|  1066.504|    60.134|\n",
      "   6|  3451.654|    75.581|   138.349|   -62.768|    -0.326|  1201.991|    75.581|\n",
      "   7|  3424.400|    84.498|   144.092|   -59.594|    -0.379|  1381.102|    84.498|\n",
      "   8|  3452.853|    73.764|   133.176|   -59.413|    -0.341|  1249.590|    73.764|\n",
      "   9|  3480.874|    64.261|   123.064|   -58.802|    -0.347|  1270.859|    64.261|\n",
      "  10|  3510.073|    54.169|   113.630|   -59.461|    -0.323|  1188.856|    54.169|\n",
      "  11|  3542.419|    43.737|   104.876|   -61.139|    -0.335|  1230.183|    43.737|\n",
      "  12|  3575.594|    32.667|    94.981|   -62.314|    -0.336|  1233.738|    32.667|\n",
      "  13|  3458.420|    72.072|   119.671|   -47.599|    -0.440|  1592.216|    72.072|\n",
      "  14|  3498.503|    54.487|   106.878|   -52.391|    -0.436|  1579.494|    54.487|\n",
      "  15|  3547.467|    33.167|    93.118|   -59.951|    -0.394|  1430.149|    33.167|\n",
      "  16|  3321.288|   122.270|   153.917|   -31.648|    -0.507|  1805.186|   122.270|\n",
      "  17|  3360.778|   102.331|   138.308|   -35.977|    -0.505|  1798.837|   102.331|\n",
      "  18|  3351.218|   107.277|   139.169|   -31.892|    -0.520|  1850.249|   107.277|\n",
      "  19|  3413.640|    74.998|   118.217|   -43.219|    -0.509|  1811.857|    74.998|\n",
      "  20|  3131.560|   218.706|   226.652|    -7.946|    -0.658|  2279.922|   218.706|\n",
      "  21|  3172.123|   192.151|   204.175|   -12.024|    -0.670|  2318.206|   192.151|\n",
      "  22|  3230.686|   153.052|   173.419|   -20.367|    -0.644|  2235.011|   153.052|\n",
      "  23|  3279.892|   121.530|   149.290|   -27.760|    -0.627|  2177.177|   121.530|\n",
      "  24|  3327.516|    91.846|   129.861|   -38.015|    -0.615|  2137.967|    91.846|\n",
      "  25|  3335.272|    87.252|   123.984|   -36.732|    -0.625|  2172.617|    87.252|\n",
      "  26|  3392.194|    51.924|   102.470|   -50.546|    -0.533|  1858.647|    51.924|\n",
      "  27|  3448.947|    21.930|    85.855|   -63.925|     0.000|    21.930|    21.930|\n",
      "  28|  3443.132|    21.932|    84.257|   -62.326|     0.000|    21.932|    21.932|\n",
      "  29|  3433.804|    21.933|    82.633|   -60.701|    -0.011|    58.808|    21.933|\n",
      "  30|  3415.413|    22.136|    85.060|   -62.924|    -0.107|   387.099|    22.136|\n",
      "  31|  3482.287|    15.038|    65.801|   -50.763|     0.000|    15.038|    15.038|\n",
      "  32|  3525.497|    15.041|    55.130|   -40.089|     0.000|    15.041|    15.041|\n",
      "  33|  3401.448|    15.044|    76.888|   -61.845|    -0.128|   450.668|    15.044|\n",
      "  34|  3316.261|    26.031|    98.885|   -72.854|    -0.780|  2612.795|    26.031|\n",
      "  35|  3379.226|   -22.575|    76.007|   -98.582|     0.000|   -22.575|   -22.575|\n",
      "  36|  3390.924|   -22.580|    69.196|   -91.776|     0.000|   -22.580|   -22.580|\n",
      "  37|  3453.876|   -22.584|    52.018|   -74.601|     0.000|   -22.584|   -22.584|\n",
      "  38|  3483.156|   -22.587|    41.942|   -64.529|     0.000|   -22.587|   -22.587|\n",
      "  39|  3499.450|   -22.592|    37.892|   -60.484|     0.000|   -22.592|   -22.592|\n",
      "  40|  3470.900|   -22.597|    38.196|   -60.793|     0.000|   -22.597|   -22.597|\n",
      "  41|  3486.621|   -22.603|    32.174|   -54.777|     0.000|   -22.603|   -22.603|\n",
      "  42|  3498.130|   -22.610|    27.045|   -49.655|     0.000|   -22.610|   -22.610|\n",
      "  43|  3521.859|   -22.617|    20.986|   -43.603|     0.000|   -22.617|   -22.617|\n",
      "  44|  3447.254|   -22.624|    24.823|   -47.447|     0.000|   -22.624|   -22.624|\n",
      "  45|  3448.858|   -22.631|    20.702|   -43.333|     0.000|   -22.631|   -22.631|\n",
      "  46|  3525.608|   -22.639|    10.306|   -32.945|     0.000|   -22.639|   -22.639|\n",
      "  47|  3585.029|   -22.648|     4.702|   -27.350|     0.000|   -22.648|   -22.648|\n",
      "  48|  3598.532|   -22.658|     2.043|   -24.701|     0.000|   -22.658|   -22.658|\n",
      "  49|  3640.963|   -22.666|     0.337|   -23.003|     0.000|   -22.666|   -22.666|\n",
      "  50|  3638.397|   -22.674|     0.000|   -22.674|     0.000|   -22.666|   -22.666|\n",
      "MSE             2782.616\n",
      "Average Error   -48.546\n",
      "Total P&L       -2475.835\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BCC97_hedge_run(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VP1y0CM/3DAP7V4uI+HA8tnU/YjIMDJMJZ736OO5uh+PONmcPrHW7CZ8xlagRQzAnJuKq\npkgbNgpnw9tPH/KffLvd2Dasx77oC8IWL8Ry+NA/b5WvgPPmejhvvgXnzbfgrlzlknMaNfBlIie8\nR8Yzvb29v5fK6SShWUOsv+4g6fOv/LKWVyAF8vtJ8eIx5/zHyPEjKqXUVKDn5VDUCC+L3kXMEz0h\nPJyUGbPP+gbguL8zacf/JHroIOLuv5ekL5dgxMUHN75fdhA9sB/2NasxwsK8U6yf6R2aAiAsjMwH\nHyJq7GjCvlhw9qOk9HRiez1B2MLPcZevQPLMubir18jV5Z11r8e2aQPW7dtw3Zi/HguK/M++bAnR\nA/rhLnUFybPnX7S3wChenOwWdxK26AusW7fguq5OkCL1P/Pe34l55QXsK74BvOtXZd3TjuzWd+Mp\nWercJ1ksZHXriePutkS9MZTwGVOI73A3jtZ3k/b6MDzlynuPc7mw/biGsEVfYP9qEZbjfwLgiY0j\nq2Mnsps0w3nzLX79BTC93wDCliwmYvy7ONrcg+va2pd0nYgP3sP66w4yH+iS74ubUMlxD45SajXe\nx1JHgala698CGZi/FNYeHFPiSRLuuB3L/n2kfDgVxz33/vcgwyCq/4tETppA9i23kjxnAYSHBz62\nv/8mauRQwmdMxeTx4GjegrTBb+CpdOEhXYHOt/ngHxS5/mpcteuQtHSlt+3wIWK7dsK2fSvZ9eqT\nMmUmRtHcD3QOmz+P2Cd6kjZ4OJmPP+3v0AMiP3++C6Lz5dt87CgJjephSk8ncenKiz8K8bF/u5y4\nTu3J7NqdtNFj/R1u4GVmEvnuW0SOG4vJ4SD7tttJe+NN3FWr5fpS1u1bie7XF9uG9RgREWQ+8gSR\n6cl4PvsM88mTAHiKFsXRsjWO1m1w3trw9KDtQLCt/o749m1w1bqaxOXf5XojTPOB/RS57SaMqChO\n/rDxshhnFYoenNyMwemstX4YeA+4Tyk1Uyn1kD+CE37mchH7SDfv2izP9T13cQNgMpE+ZARZbdp6\nBx4/+Qi43YGLy+kkfNIHFLm5NhHTJuOuXIWkOfNJmTnvosVNMHjKlSe7eQtsmzdh/Xkz1o0/kdC8\nEbbtW8l88CGSP/nikoobkJlU4hJ5PMQ89RjmkydJGzQ0x8UNQHajJrhLlyFswSeQnh7AIP3P/vVS\nitx2E1FjRuJJKELKxGkkf/L5JRU3AK6rryVp0XJSxk3AExNL5LtvweTJGFYbmd16kjR/IX9v303a\nW//D2bhZQIsbAOdtjcjs3BXrL9uJfO+d3J1sGMS82BtTZiZpQ3K/RU1hkpsC59R39lggAe9YnPv9\nHpHIs6hB/bGvXonjjpZk9Btw4YMtFlLHTSC7fgPCFn1BdP8X/b67NoBt1UoSGtcn5hXv9dOGjiDx\nu7Xebyb5yKnBxtF9nyO+7Z2Y/v6LtGEjSRvzbp6+6XkqVMRTtCi2zZv9FaooBCLGvYP9++9w3NGS\nrO6P5u5ki4WsTg9iTkslbOHngQnQz8wH/yC2ayfiOnfEfOggGU88Q+KPG3Hc3S7v44hMJhwdO5G4\nbjMp74yHNWs4uU2TNvItnA0agjU3k4rzLn3QUNwlSxE5egSW3Tl/IBK24BPsK78lu1FjHO06BDDC\ny19uCpwPlVLrgEVAInCD1jrnoyxFUIR//BGRH76PS1X3ro2RkzURwsNJmf4xrppXETFlIpHvjPFb\nPOZ9e4nt2on4Dndj+U2T2bU7J9dtIfPRJ3PdLRsMzkZNcF9ZAdu2nzHCwkmePZ/MR57wyzdXZ+26\nWP7Yj+mvv/wTrCjQrJs3EjViCO6SpUgdO/6SPoNZnR7EMJmIyO9r4jgcRI4dTZFbb/CuylyvPokr\nfiD99WEY0TF+vZURHePdjLR+/ZCuGWPExZM28i1M2dnE9H46RytPmxJPEj2wH0ZEBKmj3r78B48H\nWG7+dS3AAKCy1nrI+fanEqFjXb+O6BeewxMfT/KMORgxsTk+14iNI3nOfNxlyxE1fDAR7717SVsX\nnJaWRtTQQRRpcOM/37C++Z600WMDvuFcnpjNpA1+A0eTZiQt+Rbn7U38dmlX7VPr4Wy4yJEi5AwD\n0kK3E40pLZXYx3uA203qex9e8qNRT/krcTa8HdtP63LVSxBUDgfxbe8kavhgjKhoUsZNIPnzr3DX\nqBnqyAIuu1VrHHfdg+2ndYRPnXT+A10u7/fU1wdi/usv0vu+jKdCxeAFepnKTZ9cZ631LqVUAt4e\nHJGPmA8fIq5bZ/B4SJk0A0/FSrm+hqfUFSTP/Yz4u5oT/foAwud9TNqgYbn7IW8YhC34hKjXB2I5\ndhR32XKkDRpK9l33XDa/bWS3vNOv20Gc4qz7zzic3EwxF8FlSk0hrsPd2DZvwhMXj6dMWdzlyuEp\nWw532fLev5cpi7tsee/MxAB8rqNfeh7L/n1kPNMb522N8nStrM5dsX+3gvBZM7zrNuUz0QP7Ydv4\nE47Wd5P69v+CPpsz1FKHv4nt+++Ifn0AER9Ng6xMTA4HpqxMyPL+aTpjbKSr5lVkPn6O9Y/Ef+Sm\nwIlVSu0H/lRK3Q4sAXprrWVQQaj5tmEw/3WC1OGj8vQN0V21Gomr1hH5xhDCZ88k/r62OJo0I33Q\nMNyq+gXPtezYTvQrL2Bf96N32vfzL3mnfUdGXnI8Bck/PTiy4F++5XIR82g3bJs34bz6WkzZDiz7\n92H9dcc5Dzcio3DVugrX1dfguuY675+qRp7Ga4V9OpfwT+bgrF2H9IuNocsBR4s78RQpQvi8j71b\nigR4AG1uhH06l4hpk3HVvIqUcRMK5fcKo2RJ0ka9TXSfXpgPHcQID4fwcDxFi2GEef9unPovNo6M\nvi/ly8f7+VFuCpxngSZAX611hlKqBTAO6BGQyETOGAYxfZ7Gtu1nMjt3JavHY3m+pKdkKdLGvkdm\nj8eIfu0Vwr79Gvt3K8jq2o30F175zyMm08m/iRpxxrTvlq1JGzwcz5UV8hxLQWIkFMFVqTLWLZu9\nz9tlz5h8J3pgP8K+/RpHk2akfDTXO/DUMDAlJWI5dBDzwYNYDv2B+dAhLIcOYvl9D9bNG7GdsfeR\nYbPhql7TW+xcfQ2ua2t79yXKwb+3ef8+ol/sgycqmpQPpvjnB1lYGFkdOhE54T3sy5aQfdfdeb+m\nH1h27SSm77PehQunzCiUxc0pjnvuPf9sV3HJclPg7Nda/+5dzBi01plKKdlsM8Qi/jeW8AWf4rzh\nJtJGjPFrd7n76mtInr8Q+7IlRA3qT8TUSYTN/4SM3i+Q2fMxsFrPXi20ajXSho7067iVgsZVuy7h\n8+dh2fs77ipVQx2OOEP4pA+8y97XqEXqh1P/mVVjMnmL04QicPW1/z0xMxPrrl+xbt+GddtWrDu2\nYv31F2zbt54+xF2uPFkdO5F1f+fzF/5OJ7GPd8ecluqdznwJj5nPJ6tzVyInvEf4xzPyRYFjSksl\ntvuDmDIySJky86L7vwlxKXJT4JRRSpXhn802b0U22wwp+zfLiBo2CHfpMiRPmRmYPZtMJrJbtCK7\ncVMipk8m8s03vM+Kp07CiInB+st2PNExpA0a5i168lH3d37krHs94fPnYd28UQqcfMT+9VLvNgjF\nS5A8a16uBugTEYGrdt3TjyABcLmw7P4N6/at2H74nrAvPydqzEiixowk+9bbyOr0II4725zda/Ha\na9g2byLr3o44Onby3xcHuKvXwHn9jdhXfIP58CE8Zcr69fq5YhhE934G657dZDzxDNmt24QuFlGg\n5aaP/C3gO+BhpVQ6MB3w777vIscsu38j5rEeEBZGyrRZ/tkx90LsdjIfeYKT638m47EnMR85hPWX\n7WTd9wAn124m88lnpLjJAZdvwT+bLPiXb1h2bCfm0e4QFkbyzLl4ypbL+0WtVtw1auLo2Im0d8bz\n9/bfSHn3fbLr1ce+ZjWxTz1K0aurEf38s1g3/oTt+1UwYgTuKyuQNuqtvN//HLI6d8VkGITPnhmQ\n6+dU+OQJhH+xAOdN9UgfMCiksYiCLbebbVqBU/uxa611HuYRB0dB3KrBlJxEfIvGWH/fQ8r7k3Dc\n2zHoMZgP7MeUno67Zq2g3bNAbB3gcFCschlcNWuRtHxVSO5v//47sm9vChbLBQ8tEPm+CPOxo8S3\naIzlyGGSJ38UlMc35r2/Ez53FuFzZ2M5chgAw2LBZDKRuHAZrro3BObGaWkUvboaRkICJzdsu+i/\nfyBYN/5E/N0tMeLiSVyxBk+pK4IewymF4fOdn+TrzTYBfAXNL6deK6VGaK37XegcpZQZWAisB+x4\nH2t111pn+t7vj3c2VrEzznmBf1ZMXq61/tLXfh3wFLAPKIF3wHO+L7L8yu0m9rHuWH/fQ8bTz4Wk\nuAFkAPGlCgvDddXVWLdvg6ysoOz9dZphENPrccI/mx+0H+b5Wno6sV3ux3LkMGkDXg9aPjyVKpPx\n8qtkvNgf26qVhM+ZSdjypTB0aOCKG4DoaBxt7yVi5nRsq78L+lg5019/EdvzIXC7SZkwJaTFjSgc\nLlrgKKU8+Mbd/IvJ137BAsdnrdZ6qO96XwDtgFlKqUbAWRtpKKVuAm7XWrfy9RjtVEqtAlKAmUBT\nrfUxpdQY4CFgcg7uX2BEDR2EfcU33qnb/eUJ4eXIWed6735XO7bhuv7GoN03YtIHhH82H/BuPlio\nCxyPh9gnH8G2dQuZnbuS+cxzwY/BYsHZuCnOxk1JxfsbLgHuUcjq3JWImdMJ//ij4BY4bjexT/bE\ncuQw6a+86t0aQYgAy8kYnHe01pZz/GcG3r7YyVprzxnFjRUoC2ilVEngPuB//zqlNbDWd64L2Ak0\nBCoBEVrrY77jfgD8vxpbPhb2yRwi33sHV5WqpH4wOSRdzCLvQjEOx/rTeqJe648nIcH7etevQbt3\nfhQ15DXCliwiu0FD0ka+ddksQplXrjrX46pRk7CvFmL2PR4LhsgxI7F/twJHszvI6NUnaPcVhdtF\ne3C01r0v8F7fnN5IKXUH0BvvXlabgYlAXyDuX4eWwFvUnJLiazsBpJ6j/YISEiKxWgNXCBQv7t99\nUs5r40bo8wzExmJdtJBiVfwwEPIyFLR8B1JT72+v0b9sJToYX8/x4/DoQ+DxYFqwADp2JOy3XTnK\nZYHI979NnAjvvQNKYf/iM4r7ir78ICj5fqEvdO9O0THDYcaMwN9v6VIYMxIqVCBszscUL/Lvb/mh\nUyA/3/lYsPMdtO1TtdbLgGVKqRl497RyAo/hHWcToZTqB8wHjgNnZiHW13a+9gtKTMzwS/znEqxB\nauZjR4lvczfm7GxSps4ku0jpgHdl50cFZlBgXEmKJiRgrF3HyUB/PS4XcR07YD9yhLSBg8msVZc4\nVQP7mtWc2H8MoqLOe2qByfcZbKu/I+7JJzGKFCFxxlw8Lmu++X8paPlu2Zb4q8Zi++gjEh/sfvb0\ndj8wpSRj27Ae29ofsa39AevPm8FmI+nDabjctsKXbwEEfJDxOdsDvpSqUqqmUurMR0n7gFit9eNa\n6xHA+0Cm1nqE1no3sBio5zvXBtQAVgN7gUylVCnfder7ji243G7Cp00moeHNWI4eIX3A62Q3vSPU\nUYm8Mplw1a6LZf8+TH//HdBbRY0Yin3NahwtW5P59LMAuKrXAMD6266A3ju/sfymie3eBcxmkqfN\n9utCepcVi4X0IW8AED3wZe/Gonlg+usv7IsXEjWwH/FNb6NotSuJ69SeyHffwrppA65aV5HywRRc\n19XxR/RC5FieenCUUhGnZkNdgAPooZSqDZwqWHr5zq8CPI63B2cA8LbWep1SaqVSajje3p3ntdZJ\nvuMfBIYppQ7g3d18el7iz8+sG9YT/fIL2Lb97F1Ib8gbZD76ZKjDEn7irHM99hXfYNuyMWBFq33J\nYiLffQtXxUqk/u/90+NM3NW9uzRbdu30+2/v+ZXp77+J69wBc0oyKe99iOvmeqEOKaSc9RvgaHUX\nYV8tJOzLz3Dc3S7X1zAf2E9sz4ewbd1yus2w23HeeDPOerfgvLk+rhtuxIiWx0AiNHJc4CilXtZa\nv/Gv5klA5wudp7X+He+sqXO9twfvOJy+/2p/8zzH/0wB3/vKdPw40UNfI3zOLACyOtxP+quD8ZQs\ndZEzxeWCorWeAAAgAElEQVTEVcdbWFg3BabAMe/9nZinH8OIiCBlykyM2H/GPbiUrwdn5684/H7n\nfMjhIO6hTlgO7Ce9z4s4Otwf6ojyhbRXB2P/eilRQ17DcUer3C1ZkJVFbI+u2Lb9THaDhjjrN8BZ\nrz7O2nWDu/SBEBeQm0dU3ZRSzwAopYr7pnu3D0xYhZDLRcSH4ylSrw7hc2bhqnU1iV8uI/W9D6W4\nKYCctX0zqbYEYGfxjAziunfBnJpC6ptjcde66qy33dW9u8Jb9c5znV2wGAYxvZ/G9tM6streS8ZL\n/UMdUb7hqVSZzJ6PY/njABEfjs/VudH9Xzq9wW/y/IVk9HkRZ736UtyIfCU3Bc6DwHal1Fd4Z0Gt\n9bWJPLL98D0JTW4lekA/MJtJHTGGxG9WF/pu9ILMKFoUd4WKWLdsytEYCPPRI9h+XIMpKfEiFzaI\nebE31l93kPlwj3PuaWTExeMuXQbLroJf4ES+NYrwT+firHsDqe+8X2img+dURp8X8BQtSuTbozH9\n+WeOzgmb+zERH03FedU1pA0/Z2e7EPlCbgqcBkBPoAywFNgBBG8hhYLI5SL6+WeJb3snll07yezy\nMCfXbiar+yOyxk0h4KxTF3NiIpZ9v1/wOPtXiyhSry7x97SiWLUrKXLDNcT26ErEu29hW/ktppP/\nDFQOnzGV8HmzcdauQ9qQEee9prt6DSxHj1y8YLqMhX32KVEjh+EufyXJ02dL78I5GHHxpL/YH3N6\nGlEjh170eMuvvxDzYm88sXGkTJ4BERFBiFKIS5ObAmcE8Adwvdb6ESAemBaIoAqFrCxiuz94+jeh\npKUrSBvzLkaxYhc/VxQIpxb8s246z4J/Hg+Ro0cQ9/ADgEFGz8fIbtQYU2oKYQs/J3roIOLva0ux\n6hUpUqcWsV07Ed3/RTxFipAy+aML7i7vOj3QuGDOpLJuWE9MryfwxMSSPHMeRomLLplVaGV1eRhX\n9RqEz5qBZcf28x5nSk0htvuDmDIzSX33/cI7C01cNnIzi+oNrfWrp15orWcqpYpc6ARxbqbUFGK7\ndsL+w/dkN2hE8vSPITo61GGJIHOeKnC2bPrvwNf0dGKfeZywRV/gLlee5OmzcV91tfc9w8B8+BDW\nrT9j3bYF67at2Lb+TNjSxRhmMynvT77ojtinp4rv+rXAPQo1H9hP3EOdwOUiZfps3L6vVZyH1Ura\noGHE39+O6FdfJnn+wv8+yjMMYp57Guve38l46lmyW7UOTaxC5EKOCxyt9au+ad0VgJVAaa31u4EK\nrKAy/fUXcZ3uxbZ1C44725DyweQL/qYtCi7XVddg2Gz/2bLB/McB4rp2wvrrDrJvuZWUSTPO7tkz\nmfCULUd22XJk33mXt80wMB89gikrE3elKhe9t7uGtwenoG3ZYEpJJu7Bjpj/+ovUkW/hbNw01CFd\nFpyNm+Jo2pywb5ZjX/oV2S3P3gUn4sPxhC38nOybb5E98MRlI8ePqJRSDwPLgJfxrkHztm9dGpFD\n5sOHiG9zx+kN/lImTpPipjALD8dV6yqsO7aDwzth2/bjGhLuaHR6kHDyJ1/k7LGlyYSndJkcFTcA\nrqoKw2QqGAONXS4sv+/GvmQxsQ93xqp3kfHYk2R16xnqyC4r6YOGYVgsRA3qD9nZp9utP60n6vWB\neIqXIHXiNLAGbQF8IfIkN5/UBkBV4D2tdTbQXin1Ht4dvsVFWPbsJq7D3VgOHyLjqWdJf3WwzOgQ\nuOpcj+3nLVh/2Y51689E938RgNQ3x5L1UPfA3Tgy0juLa9ev3llcl8NnMTMTy+97sO7WWH7TWHb/\n5v3773swnfED2dG8BemDhoUw0MuTu5oi6+EeREz+kIgpH5L5+NOYTpwg9hHvPmYpH06VJSvEZSU3\nBc4xrbVHKXVmm8fP8RRI1m0/E3dfW8x//03agNfJ7HXe/UtFIeOscz0RUyYS88zjWHf/hqdoUVKm\nzPSuKRJgblUD69LFmI4fxyhZMuD3y4vwKROJfvXlswoZAE9UNK6atXBXVbiqKdyqBtlNmsksxEuU\n/sLLhH06j8jRI8lq15HYJ3piOXqEtAGDcNZvEOrwhMiV3BQ4xZVSDwDxSqkbgOaADDK+CNuPa4h9\n8D5M6Wmkjn6HrK7dQh2SyEdcdX0DjXf/hqvW1STPmI2nXPng3LtGDcKWLsaqd+LMxwVOxIT3iB74\nMp5ixchq1QZ3tWq4qirc1RSe0mUuj96ny4RRpCgZfV8ieuDLJLRsjOXgHziatyDz6edCHZoQuZab\nAucl4B2gqe+/Jfj2lBLnZl/61enu3dQJU3Dcc2+oQxL5jLtiZbIbNMRT6gpSR719wd29/X7v6v8M\nNHbe1iho982NiPH/I3pQf9wlS5H82WLcVaqGOqQCL7PbI4RPnYR17++4y19J6rgJYA74vsxC+F1u\nZlElAl3PbFNKlfV7RAWE7ftVxPboAjYbydNny2wOcW5ms3dabgi4zth0Mz+KePdtooe+hvuK0iR/\ntijHA6hFHtntpL09jsg3hpA+bCRGfEKoIxLikly0wFFK3XaBt58FpFviXyw7fyW2m3eCWfLMeThv\nvVAKhQgNd+UqGFYr1p35b6p45NtvEvXGENxlypK0YJEsKhdkznr1Sf5yaajDECJPctKDMxvQQDhQ\nC/jF114LuPAa84WQ+dhR4h5ojzklmZT3J0lxI/Ivux13lareHpx8NJMq8s03iHrzDdzlynuLmysr\nhDokIcRlKCcPVgdrrRsD64AKWutbtNa3AFfi3XBT+JjSUont3BHL4UOkv/Iqjns7hjokIS7IVb0G\n5vQ0zIcOhjoUMAwiRwz1FjflK5D0+VdS3AghLtlFCxyt9QTfX0v4xuGcak8CZH+BU1wuYns+hG37\nVjK7PEzGs8+HOiIhLurMgcYhZRhEDR9M1FujcFeoSNLni4M2m0wIUTDldpp4b2CV73UjQFZ9AjAM\nol/sjX3FN2Q3bkrayLfyTXe/EBdyeqDxzp3QrEVogjAMoga/SuR77+CqVJnkBYu807+FECIPcjP3\nrxtwC/C177+bfW2FXuQ7Y4iYOR3n1deSMmm6LGUuLhvu6tWBEPbgGAZRgwZ4i5sqVUn+/CspboQQ\nfpGbaeJHgA5ntimlKvs9ostM2CdziBo+GHfZcqTMmocRHRPqkITIMfeVFTHCw7HoXcG/uWEQNeQ1\nIt//H66q1UhasDjfr6gshLh85LjAUUpZgMZASf7p+XkQ74rGhdPKlcQ89xSe2DiSP/4UT6krQh2R\nELljseCqVh2r3glud/C2ODAMIkcMIXLcWFyVq5C8YJEUN0IIv8rNs5RFQCzeqeFuX1uh7Uu27NoJ\nbdsCkDJtFu7qNUIckRCXxl29BrZtP2PZvxd35eCsFBw5egRRb4/GXaGid8yNbOIohPCz3BQ4MVrr\ns3YAVEo19nM8l4esLOIeaA/JyaSOnyhr3YjL2pkDjYNR4ES+/eY/U8E/W4znitIBv6cQovDJzSDj\nb88x5qaaP4O5XJhcTozYOHj7bRzt7wt1OELkibuGt/cxGAONI/431rtCcbnyJH22CE8Z2e1FCBEY\nuenB6Qr0U0r9BTgAE5AAfBCIwPIzIzqGxO9+pHjxGDiRGupwhMiTYO1JFfH+OKKHvOrdfmH+Qlnn\nRggRULkpcA7hXfvmFBMwyJ/BCCGCz1O6DJ6Y2ID24ERMfJ/o117BXeoKb3FToWLA7iWEEJC7AucO\nrXXGmQ1KqdF+jkcIEWwmE+7qNbBu3ggOB4SF+fXy4VMmEt3/JdwlSpL82SI8lQr96hJCiCDIyW7i\nNYGdQHul1L/fLtzTxIUoIFzVa2DbsB7L73tw16zlt+uGz5xOTL/n8RQrTvJni4M2S0sIIXLSgzMB\neADoB6z/13uFdpq4EAXJqWUOrLt+9VuBY1u1kugXnsNTtChJCxbhrloo5yQIIULkogWO1roBgFJq\ngNZ6wZnvKaXaBSowIUTw+HugsWXvHmJ7PgQWC8nT58g6UUKIoMvNVg0LctImhLj8uPy4q7gpOYnY\nB+/DnJxEyrvv47rxpjxfUwghcivgu0IqpczAQryPt+xAZaA7MBzIANKAa4HntNbHfOe8gHfV5ARg\nudb6S1/7dcBTwD6gBNBXa+0K9NcgREFnFC+Op1gxrDvzWOC43cQ+1h3rnt1kPPEMjvs7+ydAIYTI\npdws9JcXa7XWg7XWA4BIoB2QrrXur7V+A9gC9AdQSt0E3K61Hgg8B4xRSsUppUzATGCg1no43u0i\nHgpS/EIUeK7qNbEc2A/p6Zd8jajXB2Jf8Q2OJs1If3Ww/4ITQohcCniBo7X2aK2HAiilrEBZb7Me\n8K840nx/bw2s9Z3rwjuDqyFQCYg41csD/ADcGej4hSgsXKcGGv92aTuLh82eSeQH43BVU6ROmBK8\njTuFEOIcAv6I6hSl1B1Ab2CR1nrjGe3xeKea3+trKoG3qDklxdd2Akg9R/sFJSREYrUG7htt8eIx\nAbu2+C/JdwDdUAcmQcLhfdC8EZCLfP/wA/R9FhISsC5eRLHKsgXDpZDPd3BJvoMr2PkOWoGjtV4G\nLFNKzVBKPam1Hq+UigPeA7prrU/6Dj0OnJmFWF/b+dovKDEx42KHXLLixWM4IVs1BI3kO7CsZSqR\nAGT8tJn01u1znG/zoYMk3NMWk8dD8sTpOONKyhYml0A+38El+Q6uQOb7fIVTwB9RKaVqKqXOfJS0\nD6iklCqGt7h5UWu9Tyl1qgdnMVDPd64NqAGsBvYCmUqpUr7j6vuOFUL4gdu3kKdV52KqeFoacV3u\nx/zXCdKGjsR5W6PABCeEELkUjB4cB9BDKVUbOFWw9AKW++4/y7dCciowX2u9Tim1Uik1HO8sque1\n1kkASqkHgWFKqQOABZgehPiFKBSMuHjcpcvkfC0cj4fYZx7H+st2Mh/qQVb3RwIboBBC5ELACxyt\n9e94Z039W50LnPPmedp/Bnr4KTQhxL+4q9fAvuIbTEmJcJHn5ZGjhhO2+Euy6zcgbfgoMJmCFKUQ\nQlxcsKaJCyEuA/+saHyBmVQuF1H9XyTqrVG4y1cgZdIMsNmCFKEQQuSMFDhCiNNcZ+xJdS6mlGTi\nOncgcuIHuKrXIGnBQoyiRYMZohBC5EjQZlEJIfI/d43zb9lg3r+PuAc7Yv1N42janNQJUzBiYoMd\nohBC5Ij04AghTnNVVRgm038GGtvW/UhCi9ux/qbJeOwpUj6aK8WNECJfkx4cIcQ/IiNxV6jo7cEx\nDADC5swi5vleYBikjnmXrC4PhzZGIYTIAenBEUKcxV29JuaTJ+HoUaIGv0psrycwoqJInve5FDdC\niMuGFDhCiLO4qlf3/qV5cyLHjcVVuQpJS1fgvPW20AYmhBC5IAWOEOIsbt9UcX75hewGjUha8i3u\nSlVCG5QQQuSSFDhCiLM4b74FT5Ei8NRTJM+ZjxGfEOqQhBAi12SQsRDiLJ4rSvP3zn0ULxErm2YK\nIS5b0oMjhPgv2XZBCHGZkwJHCCGEEAWOFDhCCCGEKHBMhm8xLyGEEEKIgkJ6cIQQQghR4EiBI4QQ\nQogCRwocIYQQQhQ4UuAIIYQQosCRAkcIIYQQBY4UOEIIIYQocKTAEUIIIUSBI3tRXQKlVFOgHXAc\nMLTWr4c4pAJHKVUKGApcq7W+wddWBBgB7AWqAq9orf8MXZQFg1KqMt5cbwbKAn9rrQdLvgNDKWUG\nFgLrATtQGegORCD5DhilVATenC/XWveVz3fgKKXWAVm+l26tdZNQ5Ft6cHJJKRUJfAD01loPAq5R\nSjUJbVQF0q3AF8CZmyINB77RWo8APgdGhyKwAqgIMEdr/abW+lngfqVUXSTfgbRWaz1Yaz0AiMT7\nC5PkO7CGAlvOeC35DpylWutGvv9O/XwMer6lwMm9esABrbXD9/oH4M4QxlMgaa0/Bf69lfWdwFrf\n3yXvfqK13qC1/uKMJjOQjuQ7ILTWHq31UACllBVvr5lG8h0wSqkueHO674xmyXfgXK2UekkpNUgp\ndSqvQc+3FDi5V4Kzf/Cm+NpE4J2Z+xQgwfcDQviJUqotsExrvQvJd0Appe4AFgGLtNYbkXwHhFKq\nJlBDa73gX29JvgNnpNZ6JDAEeEUpdRshyLcUOLl3HIg543Wsr00E3pm5jwUStdauEMZToCilbgdu\nB3r7miTfAaS1Xqa1bgFUVEo9ieQ7UNoCWUqpfngffd+olHoOyXfAaK1/8v3pBr7H+30l6PmWAif3\n1gJXKqXCfK/rA4tDGE9hshjvI0KQvPuVrxv5DuBZoJRSqh6S74BQStU8o9sevI9NKiH5Dgit9TDf\neKcRwBrgJ631WCTfAaGUqq6U6nFGU1Xgd0KQb9lN/BIopZoB7YETgFNmUfmfUqoh0BVoAbwPjME7\ny2QkcADvzJN+Mush73wDilcBG31NUcB7wJdIvv3ON2vtTbyz1mxADaAXkI3kO2CUUvcCT+GdufYe\nsAzJt98ppUoD4/AO6I7F+xnvA8QT5HxLgSOEEEKIAkceUQkhhBCiwJECRwghhBAFjhQ4QgghhChw\npMARQgghRIEjBY4QQgghChwpcIQQQghR4EiBI4QQQogCRwocIYQQQhQ4UuAIIYQQosCRAkcIIYQQ\nBY4UOEIIIYQocKTAEUIIIUSBIwWOEEIIIQocKXCEEEIIUeBYQx1AoJ04kWoE6toJCZEkJmYE6vLi\nXyTfwSX5Di7Jd3BJvoMrkPkuXjzGdK526cHJA6vVEuoQChXJd3BJvoNL8h1cku/gCkW+pcARQggh\nRIEjBY4QQgghChwpcC7Rjh0mHJt/CXUYQgghhDgHKXAuhcPBjE6r6X/jcix794Q6GiH8btQoO9u2\nhToKIYS4dFLgXIqwMIbe/Dmz3R3Z1HMqGAGbqCVE0GVmwrhxdpo1g40b5VuEEOLyJN+9LlHYiFeY\nFPs8j+zog2Py3FCHI4TfbNtmoXpVJ1MmG3TpEsH338tsEyHE5UcKnEtkFC1Ky/fb0JIlvPJaNKY/\n/wx1SEL4xZaFR7l1+wTu/Oh+Jn+YzmOPhbNsmRQ5QojLixQ4edGpE8MbfsVa5/V83W1BqKMRwi82\nrXZQj7Uwbx7NF/Vh5kcZ9OkTzoIFBX5dUCFEASIFTl6YTHjeGsGMsEfpvbErJ+esCHVEQuTZhgMl\nuZl1AERMncStq0fxySeZDBoUxowZthBHJ4Q40+rV33H06JHTr/fu3cPgwQOZOnUiH3009ZznLF++\nhBYtbj/9uk+fp0lMPBmQ+H78cQ0dOrTh0KFDAbn+hUiBk0eecuW5esAdPMqH9H4hGlJSQh2SEJfs\nyBETTqeJiuyDPn0wTCai3hhC7a0z+PzzDN5918748VLkCJFffP/92QXO99+vok6d6+nW7RE6depy\nznOaN29JdHT06ddjxvyPhIQiAYnvlltupWTJUgG59sVIn7MfZPZ8nH7z7+C2n1sxp+tK7v/87lCH\nJMQl2bTBRD3jR0wAAwaQVqIMMf2eJ3roICqtv4cvvoD27SNJSTHx0kvZmM65A4wQl5/iJWJzdbzz\nmutI+mb1f84/cTxnv+QuWbKId94ZTZcu3cjIyGD37t947rm+lC5dhm3bfmbJksWULVuWAwf28+ij\nT5KZmcnw4a9TtGgxihYtyg8/fM/gwW+we/dvwCJ++WUH9erVZ8OG9cTExJCdnU27dh2YOnUiLpcL\nwzCw2Wx06/bIWXH8/PNmxo4dTa9efahT5/pz3rtYseKnj9+wYT2vvz6Adu060L37o0ybNolt27by\n+uvDGT78dWrUqMnx48e55pprad685Vn32rFjO6NHv0GvXn2oWLESo0YNo0qVavTo8Rjp6Wm8884Y\nypUrz/Hjx7n11tu46aZ6ufo3+beQFThKqcrAUGAzUBb4W2s9WClVBBgB7AWqAq9orf/0nfMCEAsk\nAMu11l+GJPh/s1jIenssM5p2o+GPK7jl822Uv+eaUEclRK5tXJnBze4fcJcshSUhgazuj2ByOMhu\ndgdER1Mm2uDLLzPo2DGCtDQTgwc7MEs/sBC51rJlayZPnkDDho0pW7Yc3367nPHj32XIkBG89tor\nTJkyi4SEBL799mvGjRvLoEHDuOuue1i79gd6936Rjh0fIDY2jqpVq9GyZWvq1LkegNq163LFFaVp\n1eou1q9fy86dvzBq1FgA+vbtxU8/rePGG28+Hcd119WhatVqABiGcd57n3LDDTfRpk1bwsMjALBa\nrfTt24+YmBhatWpNgwaNcLvddO7c4T8FzlVXXX36XgkJRWjQoNHp3qePPppG2bLl6NKlGw5HFg88\n0J65cz/Har30MiWUPThFgDla6y8AlFK/KqUWA48A32it5yml7gJGA12UUjcBt2utWymlrMBOpdQq\nrXVyyL6CM7hrXcWVz7Rg4NghPNWrO581c2CNCgt1WELkyuYNJjqwDne16pyaN5X5xNNnHVM8OoPP\nPjPo1CmSESPsvPJKdvADFcLPctrz4u/zS5cuA0CZMuXYv38vSUlJpKenk5CQ4Gsvy549u08fX6FC\nxdPtF/P777tPX/+fa/12VoFzpovd+5R77rmXZ599gg4d7uf48T8pXboMLpeL/fv38dtvGrs9jKSk\nxBxm4J9YY2Pj+OijaQBUrlyF1NSUPD06C9nvXlrrDaeKmzNiSQfuBNb62n7wvQZofapda+0CdgIN\ngxNtzmT0eZHHKy4h2p3MuKGB2RZeiEDJzobtB+K5rlISrlpXnfOY8EkfUOS2myjiOMaMGZnMm2eT\nKeRC5MGRI4cBOHjwABUqVCQ+Pp7o6OjTg34PHfrjdK/HuZh9XaiHDx8iI+PsnztVqlTj8OF/Bvce\nPHjwgtfK6b1LlChJ5cpVGTVqGLfd5h2svHbtGjZsWE+PHo/RpcvDhIeHn/MekZGRZGSkA/Dnn8fO\nirV69Zp06fIwXbo8TJMmzYmNjTtvrDmRL8bgKKXaAsu01ruUUiWAVN9bKUCCr8emBN6ihjPeK3Gx\nayckRAZ0m/bixWPOeBUDXyxgGmWp0ySBe5+EOnUCdutC6ex8C3/asAGqVIeErVtOr859Vr6dTvj8\nUziwn6Ib1lC0Wzc++QTuuSeSdeugUqUQBV6AyOc7uEKdb4vFzK5dW/nuu2X8+uuvDBw4kBIlYhk7\n9m2mTZtA+fLl2bdvH6++2h+TycHGjWtJTk5mz54d1KvnHZ/SpEkjli9fhMlkomfPnvz66zYOHz6A\nUpW4885m7NunmTHjQwzD4KabrqdVq2Z8+eWXZGSk8803i6hatSoHDuxl1aqvadDgpnPe+1x56tmz\nG4MGDWLs2DEANGx4C599No8PPhhLyZIlcTiyWLVqGcWKFePEiT+ZM2cOffv25f77OzB+/HhSU0+S\nkZHC3r17SU7+k+eee5o333yTTz75CKfTSfHixSlVKj5P+TUZId5mQCl1O9AWeE5r7VFKHQRu0Vof\n9I3H2aO1LqKUGgJka62H+M77Eph0sXE4J06kBuwLLF48hhMnUs/53vz5Vt5+287XX2cQERGoCAqX\nC+Vb5N3EiTa0NjN6tAM4d75Nf/2F/YfVOO5ud7pt0iQbH39sY/Fi+aznhXy+gys/5Lt9+7v49NOF\nIY0hWAKZ7+LFY8453SGkwwOVUncCdwDPAqWUUvWAxcCpodP1fa85s10pZQNqAKvJp9rdmU5tyza6\nNTtJcr4YJSTEhW3aaOb66hceR2AUK3ZWcYPTSY8eTqpW9fDSS+GyLZsQObR8+RLS0tJYsOCTUIdS\nYIWswFFK1QXmAjcDK4EvAAW8AjRTSg0A2gF9AbTW64CVSqnhwLvA81rrpFDEnhNhq1cwc+cNXPXH\nUlq0iGTPHplPK/K3TT9Bs1duJaHhuQcg/pttxTcUuaUu9u++ZcyYLLZsMTNrlqyRI0RONG/ekqVL\nV9KuXYdQh1JghWwMjtZ6ExB9nrcfOVej1vrNwEXkX9nNWmB74kkG3xBNxZNZtGkTybhxWTRu7A51\naEL8x/HjJpKTTVSJPIKnaO0cnWPdsR3Lgf1E93se56p1TJlipk2bCK6+2s2113oCHLEQQlyYrGAR\nKCYT6a8PI7t1Gzp39TBlSha9eoXz/vs26cYX+c7mzWbq3Ggicd8hUqbNytE5mY8/hauawrpvL5Hv\nvUPVqh5GjnTQo0cEibmbISqEEH4nBU6Q3HyzmyVLMpg3z8azz4bjcIQ6IiH+sXGjhbp13WAyYeR0\naqbdTtrItwCIHDsa8769tGnjomVLF08+GYFHOnGEECEkBU6A2Rd+QcwTPTH9+SflyhksXJhBaiq0\naxfJ8eMyLkfkD5s2Wahb15Xr85z1G5DV/j5MDgfR/V8Ew+DVVx2kpcHbb9sDEKkQQuSMFDgBFj77\nI8Lnz8O+4msAoqNh8uQsGjZ00aJFJNu3yz+BCC2XC37+2ULTJ68jvvGtkJ6eq/PTXhuKJyaWsG+W\nY/9qETYbTJyYxbRpNlaskEUAhfCXzZs3snu3Pv160qQPWLNmVdDjWLDgE9q3vyvo980t+ekaYNlN\n7wAg7Otlp9vMZnjxxWwGDXLQsWME06bZyMoKVYSisNu1y0yZEtkUPbkHy7EjEBWVq/ONkiVJf2Ug\nANEDXoK0NEqVMpgwIYtnngnn4EHpqRTCH7Zs2eTbXNOrR4/HuPXW4C/of7nM/LIMGjQo1DEEVEZG\n9qBAXTsqKoyMjAvvw+MpVpzID8djPnKEzCd7geWf32iV8tCokZspU+wMHRpGZqaJatU8REYGKuLL\nW07yLXLvq6+sWE4co93+d3DWrovj/s5A7vLturY29uVLse7ZjcntxtnwdsqVM7BY4LXXwrjrLldu\n66ZCRz7fwZUf8j116kQ2bvyJTZs2sG3bz9SuXZclSxbxzDOPYjKZWL9+LXPnfkytWleTmJjI/Plz\nOXbsKAcO7Kd06bIMHz6IAwf2U6fO9fz11wneffctDhzYz5Ili4iNjaVkyVK8+urLzJw5nT/+OMC8\neTYUju4AACAASURBVLM5dOiP0xtznvLJJ3Po0+cpKlas9H/27ju8qeoN4Pj3ZrRNulgFFDficaGC\nMvyBAqKCA3GhoIiiIOJCxL33REEEFAcuUMSNoiLDiYAyXIhHRMXJEApdSbPu74+blhZKm7ZZTd/P\n8+RpcnNy79vT2+TNOeeeQ8uWrbnppmv55RdrHav777+T9evX8c47b7Drrm1o3rwFADNnvsJZZ53D\nvHlzuPTSYQwefAE//vgD1157FXvssSe77LIrv/66hokTx/P3338ya9bb7LHH3uTk1G7V9khkZqbf\nWdV2acGJsdDuexDY/wBsRYU4lyza4fmDDw4xY4aH11/38NdfBkcemcmYMemsXi1/GhEfy5bZ6Zz1\nIwDB/VTddmK3U/TQo5iGgevJidh/slZVueQSP/36BTjjDBf//SctOSJ5HX20m5Yts6N2O/ro6r+p\nlq30PXz4SC6++FJWrvyer75azAknnExWVjY9ehzD8OEj6dPnBCZPnsAee+xJhw6Hc9RRPbnoohG0\nbt2ao47qWb6/xx8fR5cuR3LuueczfPhIbr/9JkzTZOTIK8jP38yll17JQw+N4913394hlgEDBtK2\nbTtatGhJRkYGLVu2YsSIy3A6nVxwwXDOPfd8zjrrXF54YeoOrz322D5kZVlLORx44MGV1q568MF7\nOPXUMzjnnCH079+fiRPH1/GvUzdJsRZVqvP1Ph7HT6tImzsHf/ejqyyz//4hxo0r5cYbfTz3nJP+\n/V106BBi5Egf3boFMeSzQcTIsmU2rm63EICAOqDO+wkc3gnveUNxvTiVrOuvZuvb74NhcN11PkIh\nOOMMF2++6aF5c5knQSSfzz6L7wLJNa30vf0q4zXv7xfOOWcIAM2aNaeoqIgtW7aU78se7j1wOKr+\n2D/jjLN4441XGTz4AvbYY09sNhsOh4P58+ewePFCiouL67RC+FdfLeabb1bgcJi43fFdy0WaCeLA\nd5w1Didt3pwaSkLLlibXX+9j2bJi+vQJcP316fTu7ebddyUXFdGXnw/r1tk4ZP18AIJq/3rtr/jm\n2wg1b07aooWkzbbW2DEMuOEGH8cdF+DMM2WOHCGg5pW+t19lHMBut2OaJv/9t5H87f6R9t23Xfn+\nNm36j+zsbJo0iXyxyh49juHbb1fwyisvceKJ1gDiadOex+Vyc/75F3Hyyf13+lq3201xcRGw4wrh\nPXocw3nnXcAll1zCkUd2jzieaJBPzTjwd+pCKCcXx+qfsf3+G6HwyVodlwuGDPEzeLCfBQvs3HRT\nBitW2LjlFh82SUtFlCxfbqfDYUHSvrW6lOrTggNgNm1G0b0PYdu4AV/fE8u3GwbcfLOPQMDgzDPd\nvPFGCbV47xUi5XTu3JWVK7/nyScnYpomBx/cnk6dti2TsnTpEmbPnsXq1ZrRo68D4LDDOvLqq9NZ\nvvxrhg+/lIULP6OwsJDffvuVyy+/iqeemsxff/3BX3/9yR133IthGLz77tusX7+OpUu/ori4mKKi\nIt57750dEhaHw8EJJ5zMpk2byMqyFhno0aM3U6ZMxOfzEQgEyvfzxx9rKSoqYu7cDznuuL6cfvpZ\njBv3MAcd1B7DsDFnzvsccMBB3HDDrcyYMY02bXanpGQrXbvGd0B0wlcTj7VErSa+vexh55Mx6y0K\n738Y70Ujan2sTZsMhg7NoFkzk0mTvI1ywGYyrP6bah58MI3QlkIefTaPUPPmbFr1W/lzsahv04Tb\nbktnyRI7r71WQm6Ecwo2BnJ+x1cy13cqrjLe6FYTb0x8xx4PVL5cvDaaNzd57TUP2dnQv7+bdetk\nUI6ov2XL7HRqthqAwH71656qim39Ouy/rC5/bBhw112ldO4c5Oyz3RRUv3i5EI2OrDIePZLgxImv\nt5XgOBd+DiV1G8yWng4TJnjp1y/ACSfIJIGpYtYsB++/H//e4lAIVqyw09X4Cqj/+JvtORYvoun/\njiD70mHWbIJhhgF3313KYYdZSU5hcn6JFiIhZJXx6JFPyDgx8/Lwd+iIUVpKWj1mnjQMGDXKx113\nWZMEfvihzBTbkPn9cNNN6dx2WzrDh2ewcWP8WuZWr7bRtKlJ67+XAxCIcoITOLg9Zk4Ooda7Yng9\nlZ4zDLj//lIOPjjIwIFuioqiemghhJAEJ558x/UlcMBBEKz/KoT9+gV4+WUP112XweTJskJ5QzV3\nroO99w7x+efF7LabSc+ebt54wxGXv+eyZTYOPzyIQ/8EQLCeA4x3kJXFltlzKXjhZczwPBkVGQY8\n+GAp++8fZMAAWZtNCBFdkuDEUcnV15H/6SJ8J5wUlf116BDi/fetFcqvuSYdvz8quxVxNH26k3PP\n9eNywe23lzJtmofHHktjyBAX//4b2w/8ZcvsHHFEkEC7/axbDMbghHZtQ/kkTqWlGBs3VnreZoOH\nHy6lZ88Affq4+fZbeUsSQkSHvJvEUwyu795tN5P33ith/XobAwe6YtrFUVoKS5bYeeyxNAYOdDFk\nSAaLFtml9aiO/vnHYOlSO6ecsm18SocOIebOLeHgg4P07u3m5Zdj15qzdKmdww8PUvTYZPIXLsVs\n2TI2BwJsf/9Fk1P6kDvkbPBVnh7fZoPrr7e6XQcOdPHmmzJ7hRCi/iTBSQDbr2twfLM8avvLyoIX\nXvDQsWOQY491s3BhdMblFBXBJ5/YeeCBNE491YVSWdxySzr//WcwZIif3r2DjB6dwQknWBMRBoNR\nOWyj8corTvr39++w9lh6uvWBP3Omh6lT0zjrLBd//BHdxLWoCNautXHQQfXvLo2E6XJh27AB57Kl\nZN59W5Vl+vUL8PrrHu67L5177kmT80kIUS8yD0491OW6/rSPPiB38Nn4uv6PrbM+jHpMCxbYufLK\nDM4/38/VV/sqru0ZkaIiePbZND74wMFPP9lo3z7IkUcG6do1SKdOQbK3G0oRDMIHHziYNCmNzZsN\nLrnEx8CBVpdLtCXzvBW1FQpBp06ZPPech0MO2XmSEQjA5MlpTJ7s5Jhjgvj94PUaeDzg8Rh4veD1\nbru/224mzz7rYffdqz/tP/vMzsMPpzH7qTWYDidmXt4OZaJd346lX9HklL4YgQBbn5uO76R+VZbb\ntMlg2LAM3G544gkPMVibLyml0vndEEh9x1ci5sGJWoKjlMoBdgd+BNK11t6o7Lieki3BMQq20qxr\nB3w9e1M4cUpMuq3WrzcYOTID04QnnvDSunXNVeD1wosvOnnssTSOOirIkCF+OnYMkpER2TFN0+q+\nmjQpjWXLbFx4oZ+hQ/1RXXcold6QPvnEzj33pDNvXmRTBqxZY/DVV3YyMiAjA1wus8qfb7zh4Mkn\n05g2zUP79jtPnMaNS2PrVoOxBRfjmvYChQ+Nw3vBRZXKxKK+XU9OJOu2mwjl5JI/77Odzurt98Ot\nt6bz+ed2XnrJwz77pPYXMUit87shkPqOr0QkOFHp7FZKnQA8B6wGjgM+UErdr7X+KBr7TyVmTi6b\nfvglJolNmVatrEkBx41L49hj3UyY4OWYY6pu7w8EYOZMB2PHpnPggSFmzvTUqdvCMKBr1yBdu3r4\n+Wcbkyc76do1k9NP9zNsmJ927eLTFdJQTJtmDS6OVNu2Jm3bBmosN3Kkn912Mzn7bBcTJ+78775s\nmZ2zz/bDJzZC2TkE2+4bcSz14RlxGc5FX5L+wXvkDDufLe99RFVZtNMJDzxQyksvOTn5ZHe1v4sQ\nQlQlWp+yg4B9gR/CLTe9gTOjtO/UE4fFpOx2uOYaH1OmeBk9OoN77kmrdJVVKGRNMHf00W5mznTy\n5JMepk2rW3Kzvf32CzF+fClffFFMkyYm/fu7GDDAmrNHxlXAf/8ZfPKJg9NPj81lb/36BZg61csV\nV2Twyis7focxTesS8U6dghQ98hibfvkTf7ejYhLLDgyDwscmEdxjL5zffUPW7TdVW/y88/xMnepl\n1KgMxo1Lkxm8hRARi9Yn7Z9a6/KpurTWIaA4SvtOTUVFpM35wMo0YqhbtyDz5pXwww92Tj3VzV9/\nGSxYYOf44908/nga995byltveejcOfpxtGplcuONPpYvL2bAAD/jxqXTpUsmkyY5G/WK0q+95qBv\n30BM12Hq2jXIO++U8Mgj6Tz0UFqlK7F++80gI4NtXZeGEZeku4zZpCkFzzyPmZaG67lnSH/7jWrL\nd+0a5IMPSvjhBxs9emTSpUsmo0en89prDv7+WxIeIUTVovWutqtS6n+AXSmVp5Q6F2s8jtiJpn16\nknve2ThWLIv5sfLyTF5+2UPfvgG6d8/k1lvTGTXKx0cfldCrV7B8mpJYyciAs84KMGdOCVOmeFi5\n0k7nzllcfXU6K1c2rgv5TNPqnho8OPaTFu27r8ns2SXMnevgqqsyylvwli2zLg/H6yVRTWqBwzpS\ndOd9AGRdfSX2NaurLW8NnvayalURzz3n4eCDQ3zwgYPjjnNzxBGZXHllBjNmOKJ+tZkQouGK1qfL\n7cADwDBgHTACuCZK+05J/qOsZePT5sVnmJLNBldc4WPJkmI+/bSEfv0CMU9sqnL44SEmT/aycGEx\nbdqYDBrkon9/F2+84cCbFMPSY+urr6x5g7p0iU9i0aqVyVtvlbBxo8HgwS6KirYlOK4Xp9Jir9a4\nxz4Ql1i2571wON5TTsNWVEjOReeDx1Pja2w2OPDAEBddZHVdrVxZzPTpHjp0CDJ/voPjj3fz6KNp\nMjeTECI6CY7W+g+t9dFADpCrtT5aa/17NPadqnzH9QHil+CUadXKxJEE86i1bGkyZoyPZcuKGTbM\nz4wZTjp0yOSWW9L56afEtuoUFMDcufaY9B6WzVy8fXJpFBWSPXIYtr//ivoxs7LgxRc97LZbiFNO\ncfPZZ1aCY9cao7QUM5Z9ZdUxDIrGPU5g731w/PgDWTfW/juRYYBSIYYO9fP0014+/bSEWbMc3Hhj\nuoz3EqKRi+onida6qGwsjlIqMV8LGwjf/47CdLlwfrsC2/p1iQ4nYZxOa1Dsa695+PDDEjIzTQYM\ncHHSSW5mzHDUdeH1OisqgoED3Vx3XQbHHutmwYLozdRcUGDNGXTWWduuhrKt/R1KS8m8+3Yy3phJ\nkz69cCxfGp0DVuBwwNixpZxySoB//rFxyCEhHHoVQEyWaIiUmZ1DwXPTCbTbb4fL1OuiVSuTWbNK\n0NrGxRdnNIpWQSFE1aKS4CilQkqpYIVbCLg2GvtOWS4Xvu5HA+BcMC/BwSSHPfe0BiWvWFHM5Zf7\nePddJ4cdlsX116fz/fexb9UpKYHBg10ccECQZcuKufpqH7fcks4ZZ7hYvrz+x3/zTSdHHx0gL29b\nxpR7/jm0UHtS2u9UfN2Pxr5hPU1OPZH0t16v9/G2Zxhw1VU+fvihiIx0E/vP4UU294/yIpu1FDzw\nIPI/W0LgsI5R2V9ODrzyitXdNWiQi4KCqOxWCNHAROtT42attV1rbQfSgS7AyCjtO2X5jrW6qdLn\nzklwJMnF4YATTggwfbqHjz8upkULkyFDXHToAE8+6YzJqtNeL1xwgYs2bUwefrgUmw1OPjnAZ5+V\ncNppAYYOdXHRRRmsWVP3Y5d1T5XzeKxRx6aJ/4jObH31LTznXYDh9ZIz4kLcD94bk6vssrLAtmE9\nti1bCOU2IdSyVdSPUWsVptxOe/dtbH+srdfuMjLgqae87LdfiP793axfL4OPhWhsojUG5/4K9wNa\n66+BQ6Ox71TmO/Z4ANIWzMU14VFs//6T4IiST5s2Jtdea43VeeQRWLnSTrdumZx7rot33onOwGSf\nD4YPd5GTY/LYY95KV0w7HNZcLIsWFXPooSFOPtnNmDHptZ6P5fvvbWzebNCzZ4WBIS4X+Z8uYtN3\n2vpEdjopGvsYRXffj2mzkfnIg2SPuJBY9NPZdbj1Ru1PQkab70T6jOnkXjSE3PPPsVZ3rQe73Zos\nsF+/ACed5K5XciqEaHii1UV1W4XbHUqpKcDB0dh3KgvtvgelfU7AKCkh6547aNbhQHIHnm7NCyKD\nByqx2eCYY+Dxx718800Rp57qZ9o0J4ccksWYMeksXly3sTKBAIwcmYFhmDzxhHenA7DdbrjySh9f\nfllMdjb06JHJvfemUVRUdfntTZvmZNAgf5XTzZi5TbY9MAw8Iy6jYNqrhLKyyXjnTZqcdiK2df9W\n8UKT9JmvkHnzdTus0F2T8vE3KnHjb6ri63sigf0UnnPPg7S0eu/PMODqq31cdZWP/v3drFjRuKYl\nEKIxi9Z/+0mAEb6FgGXAaTW9SCnVWin1jFLq6wrbmimlnlJK3aCUelYp1arCc9cqpe5WSk1USp0S\npdgTquC56WydPpPSk/uD3U7agnnkXDwU++qfEx1a0srMhAEDrIHJn3xSzJ57mlx7bTqdO2cyblxa\nxF1YwSBccUUGRUUGTz/txems+TVNm8Idd5SyYEEx//5r48gjM5kxw1FtT1JJCbz9tpXglDPNarth\nfMf2Ycv786wZf1csp0mfXmRMfxH3ow9tK2QYuB95EPfTT+L46Udr0/r1ZF86HGPTpmp/D7vWVh0k\nWYJjNmlK/oKFeIddEtWWpcGD/Ywd6+Wcc1wsWFDLFWiFEA1StC4YHqW1Xlxxg1IqPYLXdQfeAQ6r\nsO0+YJ7WeqZSqh8wFjhPKdUF6KW1PlEp5QBWKaU+1VpvjdLvkBgOB77j+uI7ri/G5k2kv/kazmVL\nCbY/pLxI9hWXEDjwYDzDRhDRp3AjsuuuJlde6eOKK3x8+62NF1900q1bJr17B7jgAj9dulQ9kWEo\nBNdcY3U1TZ/uIT2Ss7WCNm1MJk70sny5jZtvzmDq1DTuvddLp047ZjrvvuugY8cgbdpsa2Kyr/mF\nZv87HP/hndjywfwqjxHc/wDyP1xA7tBzcS5ZRPboywHwDL4As2VLwJpLBq+XUPMWAGRfN5r0D97D\nKNhKwUuv7jRJKBtgnMgrqHaqQsuN7dc12Nevw39kt3rvtm/fIE2behk6NIOrr/Zx4YVVt6gJIVJD\nvf69lVJ7KKX2AP4pu19h25M1vV5r/Tqw/fKiJwGLwvcXhh8DnFy2XWsdAFYBPeoTf7IxmzXHO+wS\nCp94pnyb/ZfVZLz6MpkP3I39l+pne23MDAMOOyzEo4+WsnRpER07Bhk9OoNevdy88IKzUleSacJN\nN6WjtbVStdtd9+N27Bhi9uwShg/3MWyYi5EjM/jnn8pJxfTpO85c7Px0AQDBPfesdv9mixZseX0W\nJaPGUHpcH4qvrnxxomfEZXhGjSHUZjcAiu55gFBuE9I/+hDXlEk72alZ3kWV6CuoqmP/ZTVN+/Qi\n5/xB2H7/LSr77NIlyHvvlfD6604GDnTx778yLqcqgYC14r1MmCgaMsOsxxmslCoA/sPqmtpeU611\nkyq2b7+PnsBYrfUR4celQCut9ZZwS40fcAKTgFVa6/HhctOAT7TWz1S9Z0sgEDQdjgbcJO33w6xZ\n1rfafv0SHU2DEgrBggUweTJ88gmcey5ceilMnQoffwzz5xPV9aCKiuCBB+DJJ+Gqq2DMGPjjD+jR\nA/78c7vGt1NPhXfegWefhQsvjF4QAG+/DaedZh3wyy/hiCMqP79+PbRubf3y+flJNci4klAI+veH\n996D9u1h0SKrfzIKAgG4917r3Jg4EQYMiMpuU4LHAwMHwty5cMkl8MgjyXuKCBFW5Rla3y6qh7TW\n91T1hFLqxjrucwOQDWzBmhk5X2sdUEqVbS+TEy5brfz82M0Ul5eXzcaN2zdAxcDR1tVWhI+V9v57\nhHbbjcAhh1XzotRTl/o+9FCYMgX+/tvgpZec9OjhJC/P5M03S/D5YOPG6MY4ahSceqrBXXelo5Sd\nffcNMWBAkC1bKgwCDgRovuBjbMCmDl0JRfsc6tabrIsuxvXsUwTPHED+gi8ws3PKn3Yu/JomgL+d\nYst/Ox8lHbfzuxrG+CdosuonHN9/j/fcIRROfjpq3bSXXgpdu9q49FIXM2cGeeABLzk5Nb8uVpKh\nvgsKYMgQF61bm3z9dSlDhrgYOjTIgw+Wplx3XjLUd2MSy/rOy8uucnu9TtmdJTdhK+q429nAkeH7\n3cKPK21XSjmBA4DP6niMBsvx/bfkjBhKk1NOIO2jDxIdToPRpo3JDTf4+OabYubPL6FZs9gda889\nrYUhJ0zwEgzCkCGVu6ccK5ZhKywg0HZfQrvFZk3aotvvwX/wIdjX/k7WNaOo2NdgZmbiPeU0fL16\nx+TY0WTm5FLwwivlV5S12GdXmhzfg6wxo8h4/llr1ucI1rDamY4dQ8yfX0xWlkmvXpl8+WUDbu2t\np40bDU47zY1S1npxLVuavPaaNSv0qFEZBAI170OIZFKvLqoySik3cDnQDih7h+iitT6ohtf1AIYA\nfYEngEcAF/AgsBZoC9ygtV4fLn8t0DR8+0BrPaum2DZuLIxZL3JCvgH4fGSPvpyM12Zg2mwU3few\nNdC0EUiVb1zusQ+Q+dB9eIYOo+jBR2N2HPua1TTtfTRGSTGFjz6Od/D5tXp9MtW385MFZN14DY41\nv+zwnGm3E9xPUfTgo/i7/q/Ox5g3z87o0RmceWaAG24orfXA8/pKZH3/+afBgAFuTjvNz3XX+Sp1\nSRUXw/nnu2ja1GTy5MiuNmwIkun8bgxi3IJTZRdVtBKcqcCPwHHAy8AeQCetdcIv5U65BAfANHE/\nfD+Z4VWgSy65nOI77iHl2pC3kypvSLmn9CVt8Zdsff5lfCeeHNNjpb82g5zLLsZ0ucif80mtBhUn\nY30bBVtx/PA9ju++wfH9dzh++A67/gkjFGLzx18SPKh+02/995/BmDHprF1r46qrfDRvbtKkiUlu\nrvUzOzs241ECAdhll8TUt9Y2zj7bxWWX+Rg+3F9lGa8Xhg1zYbOZPPWUl4yMOAcZA8l4fqeyhpzg\nPKi1vl4pNV5rfVXFbfXeeT2lZIITlj5jOtljrsTw+yk96RQKJj1FvS4JqoGxaRMZb87Ee+qZmHl5\nADg//RjblnxKTzqFWC9Tnuj6jgajqJDm++0JoRCb9O+VJ/mLkewrR5IxYzoBtT/5cz7BuWIZgX33\nsy41r+bTusHUt8eDY9VKAu0PtcbneDw4ly/F3+2oOu3ONGHmTAcffOBg61aD/HyDrVsNtmwx8Hoh\nN9ckN5fyxKdp06p+Ws83aWLidpv895/BunU21q0zwjfr/vr11v2iIrj1VoNLLimM6/eUZctsDBni\n4o47ShkwoPo+KJ/PmhSzsNDg+efrd/VhMmgw53eKSESCE61PpLIRPrlKqTygAOgUpX2LnSgdeC6h\nNruRM3Qw6bNn0WTdP2x9YUb5HCnRlj36ctI/nA2hEJ4Rl4FpknnfnThXLCe4x554Lh6J95zzMLOq\nHvAlwLloIUYggP/wTnFJbgAK7x+LY9nXOPRP5FxyEekfziaUncOmX/6My/FjzuUi0DF8pVhREU37\n9sK+9nfy531ep4kMDQPOPjvA2Wfv+IHv9xNOdmDLlm2JT9nt339trFplsHUr5YlRSYlBixYmrVqF\naN3apHVrk27dArRqZbLLLiatW4fw+QxGjMhiyZIMJk3ykpVV30qp2Sef2Ln00gzGj/dy/PHBGsun\npcGUKV5Gjcpg0CAX06d74hKnEHUVrQTHoZQaAMwEfgdM4Kko7VtUw39UD7bMnkvuOWfiXLaUpn16\nsvXFGZUmCqwL+w/fk/HqdEpP6k+gqzXm2zvwXAj4CahwN0cohHfgYIytW3H8uoasW27A/dD9eM+/\nEM+wEYR22bW+v17KcX72CQC+Hj3jd9DMTAqeep6mfXuR/uFsAnvvQ2ivvVPz2t+sLPyduljNMLVc\nviISTie0aGHSogVYb3PRYrJgAQwfbnLiiW6ef97DPvvEbhKad991cP316Uyd6qVr15qTmzIOh7Vc\nyrXXpjNggJsZM0qiOtWCENEUrS6qL4CRWuvvlVK7Abla65X13nEUpHIXVUXGhg3kXnAOzqVfYbrd\nFEx8Ct/JtR8C5fh2BVnXX41z+TIAvAMGUjiphlw1GCRtzge4n3gc5xJrjkbT4aD0tDMpGXkFwYPb\n1zqOqiRTfddV06O74PhpFVvefh///7rH9dhpcz4gcFgHQq1aR1S+wdZ3UZH1SdzABork5WWzYUMh\nzz/v5OGH05g0yUuvXpEnH5F68UVr/y+/7KF9+7qtVm+acOut6Xz5pZ3Ro3306BFI6CX2ddFgz+8G\nKhFdVNHq7f0FOEEpNR04EfgjSvsVETJbtmTLW7Pxnn0ORkkJuRcOJu399yLfgcdD5t2306TvMTiX\nLyPUpAmeC4fjuXhkza+12/GdeDJb3p1D/ocL8PY/HUIhMl6bQbNjutHkxGNJnzE9Jqtix4J9zWoy\nnnsm6vHa1q/D8dMqTLcb/xGdo7rvSPj6nBBxctOgZWVVTm6KixMXSy0ZBgwd6ufZZ71ccUUGkyY5\nozabsGnCo4+m8fjjabzzTkmdk5uyOO++u5Rhw3xMm+bk0EOz6N/fxYQJaaxcaZMZkEVSiEoLTkVK\nqaOBu4DftNZDo7rzOmgsLTjlTBPXExNJf+8dtrz5XkTfYp2LFpI1+nIcv67BNAw8F19K8Q231GvW\nWNva33E9/QQZr0zHVlgAQCgnl63TZpZ3edVWXOq7pIRm3Tth/+tPAvsfQMFTz0dvOYOSEtI+no9t\n3T94LxoRnX3GUFKe37VgFBaQddN12Ff+wJYPF0RldfJY2r6+//rL4IILXLRrF+LRR724XHXfdygE\nN9+czuLFdmbM8NCqVXTfFktKYOFCO/PnO5g/34HPB8ccE6B37yA9egTITsJheQ39/G5oGvJVVAOA\nucC5wEVAFvCs1vrBeu+8nhpdglMmENh2VVNREbaCrYR2bVOpiFFYQObdt+N6/lnrJWp/CsdNJBDN\n1oXiYtJnvYXrxedwrPqRTd/r8ll1HcuXWuN5Ikyk4lHf7vvuInP82PLHpstF0b0P4T13SGqOCNq2\nTgAAIABJREFUWalGUp/fkSgqolnP/2H/43eKx1xPyfU3JzqialVV3yUlcPXVGfzyi43nn/ew2261\nfzvz+eCKKzJYt87gxRc9MR8zY5qwZo1Rnux8/bWd887zc/PN8Z9bqDoN/vxuYBpyF9V4rG6qTsBV\nWuv9kiG5adTKkptQiJzLLqbpcT2sWV/D0ubNoelRXXA9/yym00nxNTeQP+/z6CY3AJmZlA4azJYP\n5rN5yYptSwZ4veQOOoPmhyhs//wd3WPWld9P+pz3Adjy+iy8A8/F8HjIvvoKsi+5ECPcEiUaiKws\nCidMBsA9fiyO775JcEC153bDE094Oe00P337upk501GrsdNFRTB4sAuPB2bMiH1yA9b3gH33NRkx\nws/MmR6WLSti7VqDE09088svjetLgkisaCU4y4B9tNYXaK0b3fIJSa2kBKOoCHw+zNxcME2yLx9B\n7jkDsP/zN/4OHcmf+xkl191ErL9eVRz/YVu/jmDbdgT32rvS1VbOL78gYXPCO53kf/QpW6e9iv/o\nnhROeIKCSU9hujPJeOsNmvY+Cse3dVuBxP7LarJHDiPt3XeiHLSojv9/3SkZfglGMEj25SOgtDTR\nIdWaYcBll/l5+mkvr77qpFOnTCZMSGPLlupft2mTwZlnutl11xBTp9avi6s+mjWD55/3MmSIn379\n3EybFr1xRUJUJ1oJzmlaa/l6m4yystg64w22vDuHYNt2YBiEmjazul7uvI8t788neGC1K2rERGjP\nvdjy/jy2vj27vOvHvvpnmpx6Is2OaI97/FiM//6Le1ykp+M7/oTyh6UDBpI//zNrXafff6PJicfi\nmjKJ2r5Dp308j4w3ZpL+/rvRjljUoPjmOwjsvQ+On1aR+fD9iQ6nzo48Msgbb3iYNs2D1jY6d87i\nppvS+f33HVtF/vrLoF8/F927Bxg3rjTWc3DWyDDg/PP9vP22h6efdjJsWEaNCZoQ9RWVBEdrHf1r\nGUX0OJ2VBsoW33ALmz9ZhGfk5WBP7OKCFVe5tm1YT2Cfttj/+ZvM++6i+WH7k335CBzfLI9pDEZR\nIZl33oqxeVOVzwfbtmPL+/PwXHQxht9P1q034n7w3lodo/T4Eyi65wG8gwZHI2RRG243hROexDQM\nXBPH41j2daIjqpf27UNMmuTl00+LcbtN+vZ1M3RoBl99Zb2da22jXz83Q4b4ueUWX1INHVMqxJw5\nJbRubXLMMZksXtx4FzcVsRf1q6iSTaMdZNxQhUI4P1mAa+pTpM2dgxE+P/2HH4Hz6tFs7NmXaK/2\nl3nnrbgnPYbvmGPZOuPNasumzX6XzLtuZetbs3cYtJ1qUu38zrzjFtyTJxDYtx35878gYX02O1HX\n+i4qghkznEyZkkaLFiZr1xrceWfNSy8k2ty51uKm553nZ8wYX9xbmVLt/E52DfYqqmQmCU7DZfv9\nN1zPPUPGyy9h22q1Zwdb74LnoovxnncBZrPmUTmOXf9E1k3XUXzrHQQO61jzCypeoWaa2H9cWe9F\nHpNRyp3fHg9Njz0Kx+qfKRlxKcV3P5DoiCqpb30HgzBnjoNmzcxazU6cSOvXG1x+eQYlJQYTJnho\n2zZ+n0cpd34nOUlwYkASnBRQUkLG66+SPXUK/PgjAGZGBt5zh1B038MJvXzb/dB9uMc9TOH4SZSe\nfU6VZTKmv4j999/wnjWIYLv94hxh3aXi+e1YvpQmJx2HEQyy9dkX8fU7NdEhlUvF+o5EKARTpjiZ\nMCGNDh1CDBvmo2fPYMwXHW2s9Z0oDfkycSFix+3GO2Qo/PADW159i9Lex2F4vRgFBduSm1DIutWC\n7e+/aj1YuBLTxPD7wTSrXTgz4+WXcD/2CPY1v9T9WCIqAh2PoPj2uwHIuWIk9p9WJTgiYbPByJF+\nli8vpl8/P/fem86RR2YyZYqTrVsTHZ1oyCTBEQ2HYeDv1ZuCV95g88KlFF9zQ/lTaR++T9OjOpP+\n9huR7apgK02P70nuWadibK3j5RyGQfHNt5P/6WJ8fU+sukhhAY7lSzHtdvz/61a344io8oy4DO/p\nAwAT+9rfEx2OCHO5YNCgAPPmlfD44x5WrLBzxBFZXHNNOqtWyUeVqD05a0SDFGy3H6G99yl/nP7m\nazhW/4xt/bqIXu9+8F5sGzdglJRUupKrTrGo/cvvO7/8guxLLgSv13q88AuMYJBAxyMwc2TZ5aRg\nGBQ++jj5H36Mr88JNZcXcWUY0LlziCef9PLFF8W0amVy1lkuTjvNxYwZDr7/3lb27yVEtRI8O4IQ\n0VH4xDP4TupH6XF9y7e5Jk3AtnEDnhGXVppM0P79d7iefQrTZqPwwUeJWme/30/2lSOx/7EW2z//\nUPDiKzg/+xgA39E9o3MMER1ud6WpE4wNGzBbtkxgQKIqrVqZXHutj1GjfLz/voPZsx1Mnmzj999t\ntGljolSQ/fcPld/22SeU7EuOiTiSQcb1IIPU4qtW9e310vyw/bFt3ozpdOIdMBDPZaMItt2XJv36\n4Px6CSUXj6T4nuiuKGL/cSW5g87A/u8/BPY/AKOkBPsfa8mfNafOi4wmSmM5v9NnTCf7+qspeOr5\nhLboNJb6jgafD3791YbWNlatsn7+9JOdv/822GUXE5vNutgxFLKuLtt2MwiGLzDr2NGgc+dSuncP\n0qFDMKnWyUpFiRhkLC04IjVlZLB1xpu4Jj5G+rtv43r5JVwvv4S/Q0ecK5YTbNnKWp4iyoIHHsSW\n9+eRO/B0HOEBrKHMLAKHHxH1Y4nosG1Yj+Hx4PzyC+myaiDS0ihvtenff9t2rxf+/NOGYVhJjt1u\nzehgt1PhsUkgYPDrr1m8/77Bbbels3q1jY4dg3TvHqRbtwCHHSYtQalAWnDqQb5xxVdd69v26xrc\nkx8n49XpGOG1iAomP03pmWdHO8RyRv5mcocMwrlkEaV9T6LgxVdidqxYaTTnt2ni/GQB/l69ExpG\no6nvJFGxvrduhcWL7Sxc6GDhQju//WbjiCOCdO4cpGNH69Zk5xdKigjIPDgxIAlO6qhvfRvr1+N6\n4VlwOim56prYz5/j8ZDx+qv4eh5DaPc9YnusGGis57dRVIiZmRX3+ZUaa30nSnX1nZ8PixY5WLrU\nxvLldr791s4uu4To2DFEx45BDj88yIEHhqI9qXpKkwQnBiTBSR1S3/HVGOvbrn8i5/xBeAcNxjNq\nTFyPnTT1XVxMxisv4VyymOJb7yS0x56JjigmalPfgYC1xtfy5XaWL7d+rl1r46CDQnTuHKR79wBd\nugTJyopx0A2YjMERQogEsq/9Dceva8i87y5Cu+9B4MDql+Aw3e5tCUAwiH31z2CzEdxPbdvnmtXg\nLYVQCMMMbRv5GgpByLS2ARzdlUTO3GH89x+uZ6fgmvoUtvx8a1soRMGzLyYspmThcMBBB4U46KAQ\n551nbSsshG++sbN4sZ3HH0/joovsHHhgiO7dA3TrFqRTpyBud9X78/ngt99s/PyzjdWrrZ/r1hns\ns0+o0lVhLVumdgNErEkLTj0kzTeuRkLqO74aa327H7qPzLGRrVPl6340W998D7Amj2yx7+6EsnPY\ntOav8jLNOh+K/fffat6Zw4Gv6//wHd8Xz7BLiOfqkxnPTiHrzlsxwhPM+DsejmPlDxilpWz+bEml\nS+pTRbTPb48Hli61s3ChnS++sPPDD3YOOSRIt25B9twzxK+/bkto/vjDusx9v/2CtGsXol27ELvs\nYvLrrzZ++sm6rVplx+EwKyU8Bx0UpEOHUMyXsYgFacERQogEK7nmBoySEtLmf1Rj2dBuu297YLMR\nUPtjZmZWKhPcpy2myw02G6bNFr6cxwZG+L7NBqVenN9/R9oXn2H/6088Iy4rf71j+VIC7Q8l6gM+\nfD7KLhUK7bU3htdL6fF98Vx+Ff4uR5J1wxhczz2De/zDFD45NbrHTkEuFxx1VJCjjrKuQy8uhq++\nshKeTz5x0LZtiNNOC9CunTVfT0bGjvvo0WPbIqmmaS1GumqVlfAsXWrn6aedBAIGw4b5OPtsv3SJ\n1UBacOqhsX7DTRSp7/iS+o6vPLufgtfehkCA0rMGAWD79x+aH7o/wV12ZfPyldZ1zl4v7vFja7Xv\n4J57UTposPXA4yH33AGEWrSg8KnnrW2miX3NLwT3bVf+Gttff9Ksy2EQCJC/cGml51JBQzy/TROW\nLLEzZYqTRYvsDBwY4KKLfOy+e/J/jksLjhBCNFbNmlF6+oBKm2z//E2g3X4E2+5rJTeA4Ssl89GH\narVrX/ejyxMcw+8j7YvPCOU2wSgssJYqMYwdEpjQbrvjHTgY10vP4R4/lsKJU+rxy4loMAzo2jVI\n165B/vjD4Nln0zj22Ey6dQtw8cV+unQJxvviv6QmLTj10BC/ATRkUt/xJfUdX9XWt8dj9YGA1YIz\ncXyt9h3cfQ9Kzz6n/PUZL79E6RkDMHOrn9zFtvZ3mnXtAMDmL5dVWv+toUuV87uoCF591cnTT6eR\nlWVy8cU+TjwxkHTdV3KZeAxIgpM6pL7jS+o7vpK1vrNGXYrrlWkU3vcQ3mGXJDqcqEnW+q6rUAjm\nz7fzzDNpLFlip127EF26BOnSxZqwsFWrxH7WS4ITA5LgpA6p7/iS+o6vZK1v259/YGzZQrD9IYkO\nJaqStb6jweuFb7+1s2SJdfvqKzvNmpnlCU/XrgH22ceMa3eWjMGJgFLqWOB0YANgaq3vTHBIQgiR\nskK77wENcCbuxiwjg/JkBqzWHa1tLFli5/PP7Ywdm8amTdbCpG3ahHb6s2nTuE/oHVUNKsFRSrmB\nJ4GDtNalSqk3lFK9tdbzEx2bEEKkOufiLwnutTeh1rskOhRRCzYbHHBAiAMOCHHBBX7Auoz9338N\n/v7bVv7zhx9sfPSRg3/+MfjnHxseDzRpYtK0qXWz7lPpcW6uicNhLWLqcFjHsh5b4+LtdpOcHMjL\ni//v3aASHOBIYK3WujT8eCFwErDTBKdpUzcOhz1mAeXlZcds32JHUt/xJfUdX0ld33fdBbffDldc\nARMmJDqaqEjq+o6xvDzYa6/qy3g8kJ9vsHkzbNoEmzdT6f7PP1vrdgUC1uTcgcC2W8XHGRkwd278\n67uhJTgtgYqdeAXhbTuVn18Ss2BSuQ83GUl9x5fUd3wle33bexxPkybjKMlphieJ44xUstd3snA6\noVUr61YfaWkxHYNT5faGluBsACr+JjnhbUIIIWIoeOBBbPpWb7tcXYgk19BWtFgE7KmUSg8/7gbM\nTmA8QgjReEhyIxqQBpXgaK1LgJHABKXUPcB3MsBYCCHiyOMh45kncU1KjXE4InU1tC4qtNZzgbmJ\njkMIIRojx08/kn3TdZjuTLyDzsVs1jzRIQlRpQbVgiOEECKxAh0Ox9erN0ZJMa6nJic6HCF2ShIc\nIYQQtVI85gYAXE9Pwdi6JcHRCFG1BtdFJYQQIrECnbvgO6oHaZ9/SnO1106nuy0ZfS0l190EQNq8\nOeQMGYSv93EUvPQqAMb69TTvcECtjr3D6zseSCivJZu/WVVeptnhB2Nb92+N+2oR/rnD649oj23d\nv2z++jtCu+wKQM7QwaTN/bDqHe3k99/81bfbXn/heaTN/ZCCZ17E1+cEANzjx+Ku5crwBc+8gO/4\nCq8f9zAlV15NyZjrAUib/xE5F54X2c7CcZdcMbr89c4Fc8m9cAi+Xr0peG6aVWzDBpp1OaxWcfp7\n9aZg6ku1ek20SYIjhBCi1opvug3Hmf2xFRftvFAotO2+aWKUzQBXgREI1O7A27/e78fw+yuXqWpb\nFcrSkh3K+nwYPt92xw3suK02An6M0tLKdRIIYHi9tdtPcLvXezxQMf5QyNpWGxVebwSDGCXFUFoh\nLtOs/u9cFW8tY4gBWWyzHmSiqPiS+o4vqe/4apD1HQpV/sDenmFY8/WXlQ0GrW2O8Hdr07Smuq2N\n7V9f9uGclratTASJyA71XfH1paXbtpW1zvj9Vf+u1X2Gpqdve73PZ73e6dxWJ35/7X5/07RiKvv9\n/X7r5nBsiz8Y3BZ/Tfsq43Rue30gYK3WabdvmxYgFLKSnlowbXZwu8sfy2KbQgghGg6bzbrVtaxh\nWB+udWUYlROTMlVtq6rMzsqlp++4rT5x7iwmp7N++63q9fbKiUWtORyQlVV5m82GmdXwlrWQQcZC\nCCGESDmS4AghhBAi5aT8GBwhhBBCND7SgiOEEEKIlCMJjhBCCCFSjiQ4QgghhEg5kuAIIYQQIuVI\ngiOEEEKIlCMJjhBCCCFSjiQ4QgghhEg5slRDHSiljgVOBzYAptb6zgSHlHKUUq2Be4BDtdadwtua\nAQ8AvwLtgJu01usTF2VqUEq1xarr5cBuwCat9V1S37GhlLIB7wJLgDSgLXAh4ELqO2aUUi6sOv9I\na32NnN+xo5RaDJSt1hnUWvdORH1LC04tKaXcwJPAaK31HcAhSqneiY0qJXUH3mHbgr8A9wHztNYP\nAG8DYxMRWApqBszQWj+stR4FDFRKHY7Udywt0lrfpbW+BXBjfWGS+o6te4AVFR5LfcfOh1rrnuFb\n2edj3OtbEpzaOxJYq7UuW651IXBSAuNJSVrr14Htl549CVgUvi/1HiVa66+11u9U2GQDipH6jgmt\ndUhrfQ+AUsqB1WqmkfqOGaXUeVh1+luFzVLfsdNeKXW9UuoOpVRZvca9viXBqb2WVP7gLQhvE7FX\nse4LgKbhDwgRJUqp04A5WuufkPqOKaVUH+A94D2t9VKkvmNCKXUgcIDW+s3tnpL6jp0HtdYPAncD\nNymljiYB9S0JTu1tACquG58T3iZir2Ld5wD5WutAAuNJKUqpXkAvYHR4k9R3DGmt52it+wJ7K6Uu\nReo7Vk4DvEqpG7C6vjsrpa5C6jtmtNZfhX8Ggc+x3lfiXt+S4NTeImBPpVR6+HE3YHYC42lMZmN1\nEYLUe1SFm5H7AKOA1kqpI5H6jgml1IEVmu3B6jbZB6nvmNBa3xse7/QA8AXwldZ6PFLfMaGU2l8p\ndVGFTe2ANSSgvmU18TpQSh0HnAlsBPxyFVX0KaV6AEOAvsATwCNYV5k8CKzFuvLkBrnqof7CA4o/\nBZaGN2UCk4BZSH1HXfiqtYexrlpzAgcAVwI+pL5jRil1BnAZ1pVrk4A5SH1HnVJqV2Ai1oDuHKxz\n/GqgCXGub0lwhBBCCJFypItKCCGEEClHEhwhhBBCpBxJcIQQQgiRciTBEUIIIUTKkQRHCCGEEClH\nEhwhhBBCpBxJcIQQQgiRciTBEUIIIUTKkQRHCCGEEClHEhwhhBBCpBxJcIQQQgiRchyJDqC2lFLH\nAqdjLb1uykKXQgghhNheg2rBUUq5gSeB0VrrO4BDlFK9ExuVEEIIIZJNg0pwgCOBtVrr0vDjhcBJ\nCYxHCCGEEEmooXVRtQQKKzwuCG/bqUAgaDoc9pgGtT3D2HbfNOtepmK5aJWpb0wSt8SdzL9bPGKS\nuCVuiTt6cUeJUdXGhpbgbACyKzzOCW/bqfz8kpgFk5eXzcaNhVU8sy3Eqp+PtMy2ctEqU/+YEhf3\nzssmd9xS3/H73eITU2zi3nnZ5I5b6lvqu6Yyke2v7vLysqvc3tC6qBYBeyql0sOPuwGzExiPEEII\nIZJQg2rB0VqXKKVGAhOUUhuB77TW8xMd1/Y2bIhNliqEEEKIyDSoBAdAaz0XmJvoOIQQQgiRvBpa\nF5UQQgghRI0kwRFCCCFEypEERwghhBApp8GNwRFCxE7lAfJVX3ophBANgbTgCCGEECLlSIIjhBBC\niJQjCY4QQgghUo6MwRFC1IpMZCmEaAikBUcIIYQQKUcSHCGEEEKkHElwhBBCCJFyJMERQgghRMqR\nBEcIIYQQKUcSHCGEEEKkHElwhBBCCJFyZB4cIUTUyVw5QohEkxYcIYQQQqScpGvBUUqNA0qAIuBQ\n4Cqt9Tql1F7Ah8C6cNFlWusxiYlSCCGEENWp3JKbHffjJ12CAxRrrW8BUEpdD9wMXBF+7gGt9fOJ\nCkwIIYQQDaMbOukSnLLkJsyG1ZJTpp9SKg/IBV7WWv8Y1+CEEEKIFNYQEpdIGaZpxv2gSqk5QKsq\nnrpNaz0rXKYJ8BZwhtZ6s1IqE9hLa71SKdUKWAx00Fpvqe5YgUDQdDjsUf4N6s8wtt2v7k9QVi5a\nZaorF60ytY1J4k6euOMpFr9bdeWS+W8Sj5gkbok70pgaIKOqjQlpwdFa96nueaVULjAJuFBrvTn8\nmmJgZfj+eqXUeqwxOp9Wt6/8/JKoxFyVvLxsNm6sa7a7rT+y+n1kR7VM9eWiVaZ2MUUa987LJnfc\nDau+t6nf+R2J6P9u1ZdL3r9J9ftL7rilvlOtvmMjlu8neXlVj+9JuquolFItsJKb67TWvymlzghv\nH6KUah++7wR2A35PWKBCiHrZsKGw/CaEiL3G9j9XqxYcpVRTrXV+rIIJ+wgrrulKKYBC4A3gL+AW\npdQ3wL7ArVrrtTGORQghhBANUEQJjlKqMzATWK+U6gV8AIzWWi+PdkBa64472b4AWBDt4wkhhBAi\n9UTaRTUK6A0s11qXAH2By2IWlRBCCCFEPUSa4PyutV5T9kBr7QGqvXpJCFG9xtYfLoQQ8RTpGJw2\nSqk2gAmglOoOtI1ZVEKIWpEkSQghKos0wXkU+AQr0Tkfa7mE02IVlBBCCCEiJ19ydhRRF5XW+jvg\nAKAT0BlQ4W1CCCGEEEknogRHKXU6cK/WeqXWeiVwc3jJBCGEEEKIpBNpF9WFwHUVHr8NPAxcEO2A\nhBDbSLNzZKSehBDbi/Qqqh8qLmyptf4W+C82IQkhhBBC1E+kCc5eSqnmZQ/CyynsEZuQhBBiG7mU\nXghRF5F2UT0F/Bhe4BKgJTAoNiEJIYQQQtRPRAmO1nqBUuogoCvWXDiLylb5FkIIkVjSwiXEjiJe\nbFNr/R/wXtljpdTtWus7YxKVEEIIIUQ9RLrY5gjgdqyuKSN8MwFJcIQQQgiRdCJtwRkF9ADWaK1D\nAEqpG2MWlRAi6qQbQ4j4ieb/m/zv1k2kCc63WuvV2237INrBCCGEEEJEQ6QJTrFSaj6wGCgNbzsR\na9CxEEIIIURSiXQenF7AZ4CPbWNwjFgFJYQQQghRH5G24FyjtX6r4gal1JwYxINS6g6gZ4VN92qt\n54afuxbIAZoCH2mtZ8UiBtF4SV+3ECKe5D0ndiKdB+ctpVRPrNmLXwGO0FovilVQWuue229TSnUB\nemmtT1RKOYBVSqlPtdZbYxWHEEIIIRomwzTNGgsppW4ATgKKgJOBR4A/tNaPRjugcAuOH2usjx14\nXGtdopS6G/Bpre8Ol5sFPFNTK04gEDQdDnu0w6w3o0IHX3V/grJy0SpTXblolaltTMkUdySiFbeI\nr2T+H4jG8WqSjHGncn2LuKpyyEykXVR7aK2PUko9obUOAlcppcbXNZJw91arKp66DXgN+F1rXayU\nuhR4HLgIaw6eVRXKFoS3VSs/v6SuYdYoLy+bjRvr2ryYXX6v+n1kR7VM9eWiVaZ2MUUa987LRjPu\nSESrvpNb/c7v5LNhw7b7GzfurFRi/geq219kcUciNnHH/v0kvvWdCv+7ySiW7yd5edlVbo80wSnr\nBqqYz7rqGozWuk+ERRcA14bvb6Dy2ZkT3iaEEEIIUUmkV1G5lVI3AXsopQYopZ4GQrEISCn1cIWH\n7YA14fuzgSPDZZzAAVhXdgkRV7K6tRBCJL9IW3CuB27C6la6DvgQuC9GMQWUUo9htc60By4F0Fov\nVkp9rJS6D+sqqjFa6y0xikEIIYQQDVikCc59WCuI3xbLYAC01jtdAkJr/fDOnhNCCCHqS1pnU0ek\nXVQnAfNiGYgQQgghRLREmuB8AXgqblBKjY5+OEIIIYQQ9RdpF1Uu8KNSahHb1qLqAoyLSVRCCCGE\nEPUQaYKzP3Dndtt2j3IsopGRvm4hhBCxEmmCM3z7pRnCrTmikYk0KYlW8lJ5P1VP5pSMJHkTQojE\nijTBWayUugDrMvHxwOla61diFpUQtSDJhEhGcl7GVyT13VC/MIm6iTTBeRgruckGHgJaKaXu1Vrf\nHLPIhIgi+bAR0dJQz6WGGrcQdRXpVVQ2rfV5wL9aa1NrPR7IiGFcIiyes+aWHUveCIWID/mfEyJ2\nIm3BKVuWoeJaVC2iHIuoI3lzFCI65H9JiNQRaYJTopR6ClBKqWuB44CvYhdW6pM3UiGEqJm8V4q6\nqjbBUUqdAHwM3A4MxVoDqjPwKjA15tGJqJE3CSGEEI1JTS04Q4A5WFdNTaVCUqOUasu2lb6FEEII\nIZJGTYOMy2Yt7lHFc6OiHIsQQgghRFTU1ILzD+AF7EqpyypsN7AGHF8Zq8CEEEIIIeqqphacV7Hm\nvhmrtbZXuNmAsbEPTwghhBCi9mpKcO7Eaqn5sIrn7o9+OEIIIYQQ9VdTF9XfWmufUuo0rKupKrqL\nGHRRKaVmA5kVNrUH2gCtsRKtdeHty7TWY6J9fCGEEEI0fDUlONlKqT/DP0+usN3AumQ8FmNwXtRa\nvwqglNoHuF5r7VVKATygtX4+BscUQgiBTCkhUke1CY7WeohSqg1wL9ZcOGUM4I5YBFSW3IRdATxe\n4XE/pVQekAu8rLX+MRYxCCGEEKJhM0zTrLGQUipDa+3dblt7rfX3dTmoUmoO1uKd27tNaz0rXCYH\neF5rfXr4cSawl9Z6pVKqFbAY6KC13lLdsQKBoOlw2OsSphBCiCoYxrb7O/sIiaSMEFFiVLWxppmM\nDwRWAWeFu4gqGgwcX5dItNZ9Iih2IRUmFtRaFwMrw/fXK6XWA4cCn1a3k/z8krqEGJG8vGw2bpTm\n3HiR+o4vqe/4alj1nV1+b+cxR1ImcRpWfTd8sazvvLzsKrfXNAZnCnAOcAOwZLvn2tQ/rKoppWxA\nH+CxCtuGACu01t8rpZzAbsDvsYpBCCGEEA1XTWNwjgJQSt2itX6z4nNKqRtjGNcpwGy6AOS3AAAI\nnklEQVStdcWGzb+AW5RS3wD7ArdqrdfGMAYhhBBCNFA1dVEtqHD/8u2ebkeM5sLRWr9dxbYFwIIq\nigshhBBCVFJTF1Uh8ChwEta6VJ+Ht3cHfolhXEIIIYQQdVZTgnOp1vpvpdRArfV1FbZ/pJSaEMvA\nhBBCCCHqqtqlGrTWf4fv7q+USivbrpRKx5phWAghhBAi6dTUglPmTWCtUurr8OMjsCb/E0IIIYRI\nOjUttgmA1vpxrDlv5oZvfbTWk2IZmBBCCCFEXUXagkN41uI6zVwshBBCCBFPEbXgCCGEEEI0JJLg\nCCGEECLlSIIjhBBCiJQjCY4QQgghUo4kOEIIIYRIORFfRSWEEEJEasOGwkSHIBo5acERQgghRMqR\nBEcIIYQQKUcSHCGEEEKkHElwhBBCCJFyJMERQgghRMpJyFVUSikbMBy4GzhGa/1DheeuBXKApsBH\nWutZ4e2HAZcBvwEtgWu01oF4xy6EEEKI5Jeoy8QPBZYAJRU3KqW6AL201icqpRzAKqXUp0ABMA04\nVmu9Tin1CHA+8Gyc4xZCiEZPLgEXDUFCuqi01iu01t9U8dTJwKJwmQCwCugB7AO4tNbrwuUWAifF\nI1YhhBBCNDwxa8FRSs0BWlXx1G1l3U5VaImV1JQpCG/bCBRWsb1GTZu6cTjskRStk7y87JjtW+xI\n6ju+pL7jS+o7vqS+4yve9R2zBEdr3acOL9sAVKyBnPC2nW2vUX5+Sc2F6igvL5uNG6WpNl6kvuNL\n6ju+pL7jS+o7vmJZ3ztLnJLtKqrZwJEASikncADwGfAr4FFKtQ6X6xYuK4QQQgixg4QkOEqppkqp\nW4D/t3fvMXZVdRTHv20BQ4lF+gdBQuRlWUIiaNTGBkQeVdrUxFRFMREwIASLoYJooT76sPQhFamC\n8h/lEYFgQBQIJQQFwdJSJZiYsDBCa0KMrQrBEIoC4x97N7lOpsax95wzHNYnmdzZ5957zp6Vmd5f\n9z7n7P2B8yV9EMD2Y8AvJK0Evg98xfYLtkeAzwFXSPoWMAW4oYu+R0RExMQ3aWRkpOs+NGrHjn80\n9gNmiLNdybtdybtdybtdybtdDU9RTRpr+0SbooqIiIjYYylwIiIiondS4ERERETv9P4cnIiIiHjz\nyQhORERE9E4KnIiIiOidFDgRERHROylwIiIiondS4ERERETvpMCJiIiI3kmBExEREb2zV9cdeCOS\nNBv4BLAdGLG9rOMu9U5dOX4FcJztD9Rt04HVlNXlZwCLbf+lu172g6QjKVn/FjgE+Jvt5cm7GZIm\nAz8HNgH7AEcC5wD7krwbI2lfSub32740v9/NkfQYsLM2X7N9ahd5ZwRnnCRNBa4DLra9FDhW0qnd\n9qqXTgDuAgYXUVsJPGB7NfBTYG0XHeuh6cCttq+0vRA4Q9L7SN5N2mh7ue1vAFMp/2FK3s1aATwx\n0E7ezbnP9kn1a9fnY+t5p8AZv1nANtuv1PajwLwO+9NLtn8CjF56dh6wsX6f3IfE9uO27xrYNBl4\nieTdCNuv214BIGkvyqiZSd6NkXQmJdNnBzYn7+a8W9IiSUsl7cq19bxT4IzfgfznB++LdVs0bzD7\nF4ED6gdEDImk+cAG20+RvBsl6TTgbuBu21tI3o2QdAxwtO07Rj2VvJuzxvYa4NvAYkkn0kHeKXDG\nbzvw1oH2tLotmjeY/TTgeduvdtifXpF0MnAycHHdlLwbZHuD7TnA4ZIWkLybMh/YKekyytT3TElf\nJnk3xvbm+vga8CvKvyut550CZ/w2AodKekttHw/c02F/3kzuoUwRQnIfqjqMfBqwEDhI0iySdyMk\nHTMwbA9l2uQIkncjbF9Rz3daDTwCbLZ9Ncm7EZLeJencgU0zgD/SQd5ZTfz/IOkjwKeAHcC/chXV\n8En6MHAWMAf4EfBdylUma4BtlCtPLstVD3uunlD8ELClbtoPuBb4Gcl76OpVa1dSrlrbGzgauAj4\nJ8m7MZI+CVxIuXLtWmADyXvoJB0MXEM5oXsa5Xf8EuBttJx3CpyIiIjonUxRRURERO+kwImIiIje\nSYETERERvZMCJyIiInonBU5ERET0TgqciGiNpK2SDhtoL5C0soN+rJf0+baPGxHtyW2pI6JLN1Hu\nSxIRMVS5D05EtELSQsraNHcCLwDfodwQ7ADbJ0laRrnh3TrgvcBRwBeBTwMzgd/ZPqfuazrlpmF/\nBQ4CHrZ9/RjHnE+5Kec2yg31lgNvp9w48jngKeAq4M91fy8D+1MW1F0l6fT6nidqn98J/Mb25UMN\nJyKGLlNUEdEK2+uAvwNLbC+0/RylmNn1/BLgSWCS7Y8Da4FbgK9TCpzZkmbUl68DHqqFxheAb0o6\naozDLgPW2V5MKWT2s30vsAm42faXbD8DLAa2215k+wJgnqRTbN9eX/uq7QXAXGCupI8NNZyIGLpM\nUUXERPPr+vgMsNX28wCSnqWMvvyBUmjsI+mE+tptwGHA06P2dSdwu6QbgVtt/343x5wLbJd0XW2/\nBLxj4PlHoSweKOkR4BTKSuARMUGlwImIieaV+jgy8P2u9uCo81W2NwHUxW9fH70j20skXQ98FnhA\n0iW2b9nNcW+wfVvd395khDviDS1/wBHRpp3AFEmzJR2yB/u5D/joQPvHwMGjXyTpattbba8CVlOm\nugb7cYSkE8fY31rg/QPtWXV/k4EPAQ/uQd8jogU5yTgiWiNpCfAeYBJlZedrKEXHUspozSpgM/A1\nyknIM4FF9e1r6nPn1fYPKOf0TAY22r5xjOP9EJhKORn5UOCrtrdKmgNcXt+/HDDwvbqvl4E/2V5b\n97G+bpsCHA5syUnGERNfCpyIiP+iFji/tL2+465ExDhkiioiYjckfYYyPXW2pOO67k9E/O8yghMR\nERG9kxGciIiI6J0UOBEREdE7KXAiIiKid1LgRERERO+kwImIiIje+TfJfXBuQKvJ7QAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bdc49e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t + 1)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_run_2.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BCC97)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.426\n",
      "Bonds              1602.498\n",
      "Cost                228.305\n",
      "\n",
      "Regular Rehedges \n",
      "----------------------------------------------------------------------------------\n",
      "step|       S_t|      Port|       Put|      Diff|     Stock|      Bond|      Cost|\n",
      "   1|  3334.785|   181.929|   186.347|    -4.418|    -1.787|  6140.884|   181.929|\n",
      "   2|  3308.847|   228.296|   192.136|    36.160|    -0.353|  1397.161|   228.296|\n",
      "   3|  3257.391|   246.484|   210.867|    35.617|    -0.450|  1713.090|   246.484|\n",
      "   4|  3284.768|   234.181|   197.179|    37.002|    -0.426|  1631.875|   234.181|\n",
      "   5|  3399.651|   185.310|   156.171|    29.138|    -0.350|  1375.014|   185.310|\n",
      "   6|  3285.852|   225.136|   192.522|    32.614|    -0.425|  1620.463|   225.136|\n",
      "   7|  3351.304|   197.344|   166.841|    30.503|    -0.411|  1575.848|   197.344|\n",
      "   8|  3408.658|   173.758|   146.445|    27.312|    -0.361|  1405.020|   173.758|\n",
      "   9|  3432.936|   165.000|   136.218|    28.782|    -0.377|  1459.126|   165.000|\n",
      "  10|  3464.136|   153.260|   125.774|    27.486|    -0.356|  1387.360|   153.260|\n",
      "  11|  3525.190|   131.523|   108.899|    22.624|    -0.349|  1361.625|   131.523|\n",
      "  12|  3536.579|   127.551|   103.206|    24.345|    -0.355|  1384.215|   127.551|\n",
      "  13|  3522.552|   132.539|   103.601|    28.938|    -0.407|  1565.209|   132.539|\n",
      "  14|  3380.873|   190.176|   139.879|    50.297|    -0.489|  1844.271|   190.176|\n",
      "  15|  3348.353|   206.117|   146.822|    59.295|    -0.505|  1898.623|   206.117|\n",
      "  16|  3376.015|   192.176|   135.674|    56.503|    -0.455|  1729.234|   192.176|\n",
      "  17|  3443.098|   161.704|   114.267|    47.437|    -0.452|  1719.386|   161.704|\n",
      "  18|  3502.142|   135.088|    97.583|    37.505|    -0.429|  1639.101|   135.088|\n",
      "  19|  3539.960|   118.978|    87.569|    31.410|    -0.136|   600.342|   118.978|\n",
      "  20|  3595.655|   111.474|    73.819|    37.655|     0.000|   111.474|   111.474|\n",
      "  21|  3465.029|   111.490|    99.232|    12.258|    -0.521|  1915.697|   111.490|\n",
      "  22|  3510.036|    88.437|    85.421|     3.016|    -0.085|   387.738|    88.437|\n",
      "  23|  3574.016|    83.055|    70.160|    12.895|     0.000|    83.055|    83.055|\n",
      "  24|  3629.452|    83.070|    58.995|    24.075|     0.000|    83.070|    83.070|\n",
      "  25|  3514.418|    83.088|    76.891|     6.198|     0.000|    83.088|    83.088|\n",
      "  26|  3452.003|    83.109|    86.759|    -3.650|    -0.394|  1442.072|    83.109|\n",
      "  27|  3470.424|    76.250|    80.896|    -4.646|     0.000|    76.250|    76.250|\n",
      "  28|  3424.919|    76.275|    88.759|   -12.484|    -0.318|  1165.544|    76.275|\n",
      "  29|  3421.872|    77.658|    85.516|    -7.858|    -0.158|   619.007|    77.658|\n",
      "  30|  3145.398|   121.602|   188.305|   -66.703|    -0.787|  2596.273|   121.602|\n",
      "  31|  3043.384|   202.719|   246.126|   -43.407|    -0.806|  2657.092|   202.719|\n",
      "MSE             730.419\n",
      "Average Error    10.551\n",
      "Total P&L       538.086\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BCC97_hedge_run(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jb4q4OcWKU5IC5z/AdxiFzmiMx7iD3h4CCPT6nGq7jkVs/w3wTRHv/QSc1i0x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\nAkdEREQSjgocERERSTgqcERERCTh/D/OVC/K7BF9egAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109c60240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t + 1)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_run_3.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10be15f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run 13_dyh/BCC97_lsm_hedging_histogram.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run  1000   p/l   33.596\n",
      "run  2000   p/l   -2.115\n",
      "run  3000   p/l  -17.951\n",
      "run  4000   p/l    2.579\n",
      "run  5000   p/l  -35.642\n",
      "run  6000   p/l  -16.109\n",
      "run  7000   p/l   26.779\n",
      "run  8000   p/l   14.318\n",
      "run  9000   p/l -506.078\n",
      "run 10000   p/l   45.902\n",
      "\n",
      "SUMMARY STATISTICS FOR P&L\n",
      "---------------------------------\n",
      "Dynamic Replications        10000\n",
      "Time Steps                    150\n",
      "Paths for Valuation        150000\n",
      "Maximum                   143.354\n",
      "Average                     4.343\n",
      "Median                     15.136\n",
      "Minimum                 -1014.275\n",
      "---------------------------------\n",
      "CPU times: user 52.8 s, sys: 7.9 s, total: 1min\n",
      "Wall time: 57.4 s\n"
     ]
    }
   ],
   "source": [
    "%time pl_list = BCC97_hedge_simulation(M=150, I=150000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HliTtG+YuX9vuLqifwQLBMuBM4BBgdr91bx7iMbcCH83MuwAiYjFwF3BCZs7qv3FETAdm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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c779ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_histogram(pl_list)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_histo.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:training@tpq.io\">training@tpq.io</a>\n",
    "\n",
    "**Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://python-for-finance.com\" target=\"_blank\">Python for Finance @ O'Reilly</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Listed Volatility and Variance Derivatives** |\n",
    "<a href=\"http://lvvd.tpq.io\" target=\"_blank\">Listed VV Derivatives @ Wiley Finance</a>\n",
    "\n",
    "**Python Online Training** |\n",
    "<a href=\"http://certificate.tpq.io\" target=\"_blank\">Python for Algorithmic Trading University Certificate</a>"
   ]
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